I think that whatever happens, the Asian vote will go in the same direction as college-educated whites. Because it seems difficult for the GOP to win in the future without college-educated whites, I think Asians will eventually trend toward the Republicans as the party moderates.
This is the key. As immigration declines, I would expect racial/ethnic categories to become broadly
less significant as voting demographics with time. This will really accelerate once Trump is out of office. Think of what happened with the 1890-1920 wave of European immigrants after 1940 or so.
Currently, the next strongest divide is education. If we are in a long period without a major economic crisis, like 1939-1979 or 1894-1929 or 1826-1857, I think the education divide will just keep building until college grads are the Democrats' single strongest demographic. However, with the broad consensus on the value of a college degree now starting to erode, the share of the population with college degrees will quickly level off and could even start declining into midcentury.
Of course, you will eventually run up against BYU, Hillsdale, Liberty, and Texas A&M, but it wouldn't shock me at all if the college grad vote as a whole is ~80D/20R (college whites specifically being ~2:1 Dem) in a tied 2040 election, with non-college being about ~67R/33D. At least until the next economic crisis scrambles things, I expect GOP gains to be first among the remaining non-college white Dems and then heavily among black and Hispanic voters without college degrees, probably to the point that the Hispanic vote is a toss up and they are getting 35%+ of the black vote in 2040.