Looking at the CGI models of the chariot bugs and the sand beetle prop
They are quite distinct from one another, the differences are larger than I remembered.
Chariot bugs aren't too dissimilar to other arachnids, when you factor in tankers and brain bugs, it's only the warriors and hoppers which look similar.
Uh, those don't look that dissimilar to each other. They appear far closer than the Chariot bugs look to any of the other Arachnid castes. The fact that few, if any, Arachnid casts actually look like they belong to the same species or even related species but instead seem to be random anthropoids slotted into a given role further lends credence to the idea rather than distracts from it. Why do they all look so different? Because they all were different species from different worlds until the Arachnids assimilated them.
And I will note you yourself commented on how it was a "common misconception" to assume both bugs were one and the same so the differences can't be that massive.
The sand beetle planet also seems to not been invaded by bugs, as it's never mentioned to be attacked. I can only assume the "Arkellian Sand Beetle" comes from...Arkellia? A place we unfortunately never get to see.
Which means we can't say for certain if it was conquered by the Arachnids, either in the present or distant past, or anything. For what little the movie says Arkellia could be the Bug's homeworld.
Memes aside we never actually get proof of the bugs invading a single planet, they seem more than content to just sit on their own planets and do...Bug stuff.
If we ignore Buenos Aires and the destruction of zegema beach in Starship troopers, Behemecoatyl desire to destroy humanity in Starship Trooper 3, Trig's destroyed home town in Starship Troopers invasion, the apparently common occurrence of Arachnid spores seeding Federation worlds in Starship Troopers Traitors of Mars. The Bugs have always been portrayed as hyperaggressive monsters obsessed with wiping out humanity.
In contrast we see the Federation actively tries to avoid war with the Arachnids establishing a quarantine zone for the Arachnid empire to inhabit and colonize and even the state approved media openly questioning on the eve of war if a "Live and let live" approach was better than invading Klendathu.
The spores they fire into space must take hundreds of years to reach other planets.
Eh chalk it up to scifi writers have no sense of scale or the Bugs are more capable than the Federation at the time suspected. Which makes sense since they didn't even seem to believe the Arachnids were intelligent before the Bug War.