All I can really say is that Brassard said the vagina would become self-cleaning, and it has. The smell and feel/texture of the vaginal walls is very similar to my wife's (she has more ridges in there, but that's a matter of some personal variation anyway) and stuff definitely does work its way out on its own. Possibly a bit more slowly, since there's also some gentle muscular contractions in cis vaginas that are less common in ours, but I've never had to make a special effort to remove even the lube from dilation. As for shedding dead skin in there, well, I obviously don't know for sure what's happening, but little nasty clumps of dead skin and whatnot came out in the bath/shower for a while immediately post-op and then... stopped.
The gyno who does my checkups for insurance says it's more or less the same as the menopausal women she examines - somewhat more dry and a bit less elastic than the vagina typical of a younger fertile woman, but within normal range nonetheless. And the swabs my GP has taken suggest that the bacterial balance is also basically normal.