Describing what my world would look like would take awhile (I've though about it a lot). For a start, here is what science would be like in my world.
PHYSICS/MATHEMATICS
Non-Euclidean geometry was invented by Euclid himself in the classical era, and not lost, because his book Geometry of a Sphere survived into the Middle Ages. Also, physics advanced a bit more quickly, since Isaac Newton did not lose his early work when Cambridge was evacuated due to the great plague of London. Pierre de Fermat also lived to write down the proof for his last theorem. Einstein won the Great Debate in my world, and Quantum Physics is only a fringe theory. Einsteinian Physics was finally replaced by Holistic Physics, developed by Prof. Nathaniel Reiter and Dr. Philo Mace, in 2008. The Reiter-Mace Equations conclusively proved gravity was a particle, not a wave, and redefined our understanding of math and physics, creating a new, integrated view of the universe that explained things both macroscopic and subatomic. Science in this world not as politicized or dogmatic, and accepts the existence of God and the supernatural.
The Teleforce technology of Nikola Tesla and Harry Grindell Matthews was perfected and released to the world. Instead of using batteries, most devices that are not regularly plugged in draw their electrical energy from the power plant through the air. Since missiles became obsolete, teleforce rays are the ultimate weapon, and only the USA has them. America guarantees never to use them, unless another country starts developing WMDs. Anti-gravity was first pioneered in the 1920s by Edward Leedskalnin and Thomas Townsend Brown, It was perfected for mass production in the 1990s independently by Ning Li, Timir Datta, and Eugene Podkletnov, and is now found in many different placed in society (though not in flying cars, for many practical reasons), The first forcefield generator was developed in 2018, and the first stardrive capable of reaching the speed of light in 2019.
ENGINEERING
Engineering in my world prioritizes making things long lasting and user-friendly rather than versatile. Instead of creating complex devices which can do many things, but take an expert to fix and need to be replaced regularly, devices in my world last for years and year, and are designed to be idiot-proof and very easy for an average person to maintenance, though they are usually simple and have only a couple of functions. Engineers in my world work on the principle that all machines will inevitably fail, and so all parts of the machine should be easily accessed and replaceable. Most systems are designed to be monitor by humans, with very few automatic safeties and controls, and very little under computer control. Engineers work on the assumption that computers will make more mistakes than humans, and can never be fully trusted. Automatic safety devices in general (like truck engines that switch off if you get out of the vehicle) mostly do not exist. Automation is heavily restricted by law, to protect people's jobs. Doctors still use physical charts, and automatic checkouts are much fewer. Florescent light never caught on, and most lights are still incandescent.
I'll mention transportation here. The Great Trolley Car buy out of the 1940s did not happen, and Victor Gruen's walkable cities movement took off in the 1950s. Modern cities look much like Disney's conception of the future from Tommorrowland or Epcot. Most people travel by anti-gravity elevated trains, subways, or other public transport, or they walk, because nearly everything you can need is within walking distance. Cars exist, but are still toys for the rich, and look very much like cars from the 1920s and 30s (except with built-in GPS). Electric cars were never invented. For long journeys, people usually travel by steam train, by ship, or by dirigible. Airplanes exist, but mostly for the military. Passenger planes do exist, but only as luxuries for the rich (as such, they are nicer and more spacious). In the country, trucks are common, but most people still ride and use horses.
SPACE SCIENCE
The space race never ended, only getting scaled up and up and up. In the present day, there are multiple space stations, permanent bases on the Moon and on Titan, mining bases in the asteroid belt, and colonies on Mars and Venus (both of which are habitable in my universe, as they were originally believed to be). Expeditions have been sent to both Europa and Uranus. Construction is underway on a permanent base on Ganymede to study Jupiter. With the discovery of light speed travel, an expedition has recently been sent on an eight year round trip to Alpha Centauri. Orbital satellite laser weapons have rendered missile warfare obsolete, Pluto is still a planet, and Ceres is a planet as well.
MEDICINE/GENETICS
Because there is no artificial division between magic and science, many methods of medical treatment dismissed IOTL are practiced here. Demonologists, for example, have the same status as neurologists. Geriatric medicine is less advanced, since it is considered socially improper to live into extreme infirmity. Most people are expected to die in their 80s. In contrast, there is a strong emphasis in this world on having children, and keeping the children as healthy as possible. As a result, obstetrics and children's medicine are more advanced due to more funding. Homosexuality, and all other forms of deviant sexuality, are classified as mental disorders, and there are numerous highly effective treatments to help people return to their normal sexual orientation. Transgender surgery is non-existent, and would be considered malpractice. Abortion is totally illegal in any case where there is any chance that the child can be born alive, no matter how small or the risk to the mother. Biowarfare research has been totally forbidden for decades, and any such development is punished ruthlessly. As a result, many diseases such as Covid and AIDS do not exist at all. STDs have been nearly eliminated. Large tax deductions are available for those who donate blood and organs, and so there is an abundance for doctors to use.
Because Macro-Evolution is well-known to be a myth, genetic research is much more advanced. Gene mapping has led to the creation of a universal anti-biotic which no bacteria can become immune to. It is sold over the counter in any drug store. Genetically-engineered microbe colonies have been created which feed on Plaque, and make teeth brushing unnecessary. Genetically-engineered crops and farm animals are even more productive than IOTL. Tailored retro-viruses have even being created to remove bad genes from embryos, totally eliminating most genetic disorders. Eugenics is still a well-respected science, and as a result of this and genetic modification, most people are healthy and good looking. Allergies are much rarer.
Of course, to be fair, it helps that society in my world is generally much healthier. All recreational drugs, including marijuana, tobacco, and alcohol are illegal and have been stamped out. Nearly all children are involved in boy and girls groups that include wilderness survival and hand-to-hand combat training, and schools provide healthier food and more physical activity. Mental health is also much better for a wide variety of reasons, mostly coming from the absence of the liberal left in society and the fact that most people are very religious.
COMPUTER SCIENCE
Generally speaking, computer science in my world is about 20 years behind OTL. This is because I learned how to use computers as a teenager, and I have resented nearly ever update made to Firefox and Microsoft since then. Also, the touchscreen and touchpad were never invented. Laptop computers come with built-in mouse and power-cord, and are larger. Keyboard designs favor large bulky keys that are widely spaced to keep people from pressing the wrong key accidently. All phones are flip phones, and the only functions they have besides calling are camera and flashlight. Texting does not exist, nor does most social media. DVDs are only just beginning to replace VHS tapes, but they are all scratch-proof. Digital animation is still developing, and most animation is still hand-drawn. There are no cyber-tvs.
On the positive side, research is ongoing into intelligent computers which can answer questions and fill requests (similar to OTL Alexa or Google Home, but they are still in development ITTL since they are not smart enough yet). Research is also working on the creation of microscopic robots to monitor people's health. While the technology is currently more advanced than OTL, it is being help up due to concerns about effects on people's health, and possible privacy issues.
ARCHEOLOGY/PALEONTOLOGY
Creationism and the young earth are universally accepted by the scientific community, while evolution and the big bang are looked on the same way as flat earth theory. It is fully accepted that the Earth was created in the 4010 BC (not BCE, that dating system does not exist) and that dinosaurs were contemporary with humans, dying out for the most part after the global flood due to climate changes. Some lingered all the way to the middle ages, becoming the origin of dragon legends. Dinosaurs also accept to be reptiles. The existence of unicorns and giants are also well-established, and many experts believe mermaid stories may also have roots in real history. Historians take more the approach of Herodotus instead of Thucydides, reporting all the different version of historic events and letting the reader judge which one makes the most sense to them instead of only reporting the version they agree with. Oral legends are also treated as history unless directly contradicted by archeology. A tablet was discovered with text in both Indus Valley script and cuneiform, which has allowed that language to be translated. The Voynich Manuscript has also been translated. Mantheo's King List and Aristotle's treatise on comedy have not been lost. Rudyard Lynch is regarded as one of the world's greatest historians in the present day.
ENERGY RESEARCH
Although people do respect the environment (there are national parks, nearly nobody litters, and actually endangered species are protected) environmentalism is far less powerful, and there are far fewer restrictions on the use of fossil fuels like oil and coal. Because of this, wind power and geothermal power are much less developed technologies, and hydroelectric power is less common as well (there is no hydroelectric dam on the Nile or Niagara Falls, but Hoover Dam still exists). In contrast, the home solar industry is booming due to less government legislation, and nuclear reactors are more advanced and more common. In fact, the Earth is currently experiencing an energy glut instead on an energy crisis, meaning there is little interest in developing energy-saving technology. Recently, in 2019, the world's first fusion reactor was successfully demonstrated, and work is actively underway on trying to mass produce it. Man-made global warming is well-known to be a myth in my world, and technologies to reduce carbon footprint are also much less advanced due to there being no interest in developing them.