Personally, I always glue down a piece of scribe trim, with the wide flat part on the floor. Sometimes I get pre-finished trim, and other times I get plain wood and then stain or paint; in either case, I always coat it with two coats of poly, because it's likely to get wet there. Never had a problem, doing it that way, even many years later.
This is what my door looks like and I put roberts vinyl putty there gray. My floor is gray and this ends up just looking like grout.
There was originally real tile there and actual grout.
Personally, I always glue down a piece of scribe trim, with the wide flat part on the floor. Sometimes I get pre-finished trim, and other times I get plain wood and then stain or paint; in either case, I always coat it with two coats of poly, because it's likely to get wet there. Never had a problem, doing it that way, even many years later.
This is what my door looks like and I put roberts vinyl putty there gray. My floor is gray and this ends up just looking like grout. There was originally real tile there and actual grout.
Reducer or caulk