Progress—in the capital P, 19th century sense—generally means that we're making outcomes more predictable, in addition to better, by removing negative possibilities. Widespread literacy? We've removed illiteracy and now the job market caters almost entirely to literate people. Insulin? Now diabetics live more like non-diabetics.
Consequently, interesting tragedies no longer happen. Publicly-funded fire departments prevent whole cities from burning down, so they no longer get rebuilt or redistricted. Plagues no longer wipe out the urban working class of cities, suddenly changing the fortunes of entire countries.
These factors majorly feed into the general sense that stable civilisations last forever and inevitably result in the end of history (not to be confused with the end-of-history illusion, which is about personal growth.) This is not fully correct—global collapse is a very real risk that's just a few edgy billionaires away from becoming the horrible present—but there definitely are certain things that will outlast any amount of political fuck-up. With regards to these things, we're finished—complete, unlikely to change in the foreseeable future.
Topic number one is human biology. In the past it was common to see satirists musing that labour would sculpt us, in a rather Lamarckian sort of way, into optimising for certain body types. Big eyes and hunched backs for sitting at a terminal; stronger necks for wearing heavy VR headsets; always, an anxiety around general atrophy. To dismiss these ideas, we need not bother engage with the obvious Luddite fearmongering being pushed in them: humans, like all mammals, are subject to sexual selection, and therefore the shape of future generations is anchored in the social conception of how a human ought to look and function. Nobody's going to get laid—much less married—because they have strong neck muscles!
True natural selection is now limited to whatever makes us infertile or dead. Bad teeth are the best example of this: hominid skulls from before the rise of agriculture had excellent dental records. This refining pressure is gone; now, orthodontia is a free variable, and something we can correct with medical procedures. The future, therefore, is one of barely-functional, highly diverse birth defects that we correct post-partum, if at all; a dependency on medicine, but not one that feeds into any particular narrative about human pursuits.
As for sexual selection, it is entirely prone to chasing fashions. Humans have a peculiar mode of sexual dimorphism not present in other primates, and are anatomically quite dissimilar to them, but between the two sexes, it is probably correct to say that the male body is less innovative: chimpanzees and gorillas of either sex have few of the secondary sexual characteristics that mark out female human bodies. If this is correct, then the trajectory for human evolution is a sort of drift, where all human bodies are gradually being toward a feminine form: furless, wide-hipped, youthful, facially neotenous, clean-faced, and full-scalped. Certainly contemporary Western beauty standards for men are headed this way. As one sex is sculpted by the other, the desires for the new sculpture are imprinted upon the new form, and reflected back upon the sculptors. Estrogen need not be in the water to provoke market demand for feminised males.
The second regard in which evolution is dead is language. The rate of evolution has been on a downward trend for centuries among literate societies, such that texts in English from three hundred years ago are basically a matter of awkward phrasing to us—this same interval did not hold up three hundred years prior. Microvariations, mostly of the loss-of-pressure variety, do still occur: YouTube has shown that the American Midwest is now a wasteland of defective idiolects and sloppy elocution.
But written language and recorded audio are too omnipresent, too permanent to let spoken language truly innovate now, and so we should never expect English to ever undergo any more changes that render the present standards mutually unintelligible with its future use. A key part of this staying power is its prestige in certain academic disciplines: Millennial English, as the language of the biomedical research and computer science literature, is as fossilised as Classical Latin; we already consider certain innovations and neologisms unacceptable in academic writing while tolerating those that were fresh in the time of our parents. This is great news for enthusiasts of broadcast television, in much the same way the success of Plato was great news for enthusiasts of Aristophanes; in both cases, the enduring need to read the former ensures an enduring accessibility for the latter. (We should probably bemoan that so much of broadcast television, and indeed modern academic research, is unworthy of commemoration.)
It is probable that automatic translation by artificial intelligence will largely erode the long-term anchoring effect of academic literature, but there is no obvious reason why it should impact the pure everyday inertia in language use that has carried us since the 18th century.