The much tinier population, given that genetic exchange between the two sets was made utterly impossible, would also drift and evolve. Perhaps (not guaranteed!) they would solve the same problems that the majority solved, but without the same kind of brakes on. That population would tend to change a little faster.
BUT if you gave a neanderthal a modern garb and a haircut, (s)he could pass as “an odd sort of guy or gal,” and that’s with a starting population way smaller than 250,000. In other words, we spent perhaps one hundred seventy-five of the last hundred thousand years diverging from neanderthals, and they from us, then we out-bred them.
((One interestjng theory: their Y chromosome failed in some way during cross-breeding, hence their male line had that little drag on it while our male line may have done fine when the cross-breed went the other way. Two-hundred-thousand year walk off the end of a one-hundred-seventy-five thousand year pier, if you will.))
In sum, yes a new species would diverge from H sapiens. But it would likely take at least many hundreds of thousands of years, if not longer. Why so slow? That would depend on whether or not we can stave off climate change. THAT kind of challenge should drive changes at a more rapid pace.
COMPARISON: Over the last two million years there were about ten successive waves of major climate change which required significant readjustments in how a member of any genus (just considering homo for now) found food and shelter. Different species of plants, prey, and predator, not to mention new problems in staying cool or warm. Our ancestors had the tools (hands, binocular vision, and I’m sure a lot more) to make brain growth a good answer to the need to adapt. Ten cycles of that, and we went from early homo whatsis to modern homo sapiens. Populations away from Africa diverged into neanderthal, denisovan, etc. The survival funnel which narrowed the Y chromosome lineage to one line, i.e. “Adam,” took place 70 to 75 thousand years ago, after which point modern H. sapiens spread into Europe, Asia and, 50 to 55K years ago, Australia.
Climate change hit us ten good licks; number eleven looms.