Generally speaking, unless in the most extreme cases I'll avoid going with "everybody dies." It's a boring answer and somebody else will chime in it with it in every single thread anyway. As a result, you'll usually find me fielding optimistic opinions.
As far as native populations, well that's a guess. Estimates on how many pre-Columbus natives there were vary by a couple of orders of magnitude, with a majority putting them between 50 and 100 million across both continents, around 5-10 million in the US. From what I've read, I find the evidence more compelling that they were on the larger side of the estimates. On top of that, the conquest of the new world heavily relied on constant waves of new colonists, more weapons, and more advanced tech flowing from Europe that won't be available here.
Presuming Manhattan has a 50% death rate we're looking at 2 million Manhattanites. Presuming similar casualty rates from smallpox, measles, and the like (I'm not 100% certain this will actually happen, those diseases aren't nearly as common in modern populations), we're looking at somewhere in the half a million and a million surviving Native Americans in the US itself. I've seen studies suggesting around 2 million surviving natives in Mexico alone so I find that pretty low, and it could be higher but let's go with 1 million.
So on paper, it would look like the Manhattanites will absorb the natives. However, now we enter into the cold facts that disturb Tumblrinas and Blue Checkmarks. Opportunities to have children will not be evenly distributed. Native Americans will start initially accustomed to having large families to make up for the heavy rate of infant death common to ancient cultures. Manhattanites will start initially accustomed to having tiny families or women avoiding children entirely in favor of their careers. While the Manhattan attitude will certainly change to suit the new reality, it won't happen in a day so they start at a disadvantage.
Beyond that, Native males are going to look a lot more attractive to Manhattanite women, while the reverse will not be true. Previous markers of status and desirability are now worthless while Native skills at obtaining food, clothing, and shelter will be the actual markers of mate value. "Big bank account and shiny sports car" will mean nothing next to "Good hunter who bags deer every week." In terms of physical attractiveness, a huge number of early writings emphasize how incredibly hot natives were, which is understandable because they just lost 90% of their population and only the fittest, strongest, and healthiest survived. Further, when inevitable combat begins, males will be on the front lines getting killed reducing their numbers and desirability further while natives will try to capture or lure females to add to their tribes. This effect will take place almost immediately as people are forced out of Manhattan and into the wilds to expand the food supply.
As a result, despite the initial numerical disparity, we can expect Native males to be significantly more genetically successful than Manhattanite males for a generation, perhaps two or three, and that will be enough to give them a huge head start at assimilation. This will also directly feed into the dominance of Native culture; the assimilated Manhattanites are more likely to follow Native customs, participate in Native worship, and learn to speak Native languages. Some aspects of Manhattanite culture will survive and be picked up by the Natives, of course. Basic ideas like Germ Theory and the Scientific Method require no actual infrastructure and things like forging bog iron can be picked up readily from library books. As I suggested upthread I suspect they'll drop all the way down to around very early steam/beginning of the industrial revolution and have advanced a bit from there by the time Amerigo Vespucci comes knocking.
We have 100% proof they had a large settlement at
L’Anse aux Meadows in 1021AD. We've found evidence of somebody using metal tools, roasting bog iron, and building possible longhouses
400 miles south of there. There's evidence they hit
New York in the form of multiple finds of items like iron spearheads as far south as Minnesota, Wisconsin, and Ontario. The big question is if those were traded to Natives who carried the spearheads hundreds of miles further south or if the Vikings were there personally, but there's no question they were fishing off the coasts of North America and had some camps and settlements.