As far as I know, both Pydantic and marshmallow start using annotation
for runtime type after PEP 563 is accepted. Am I right?

Not quite, pydantic was released in June 2017 (see HN post: https://news.ycombinator.com/item?id=14477222) and always used annotations, PEP 563 was created in September 2017, a few months later.

I can't speak about Marshmallow, back then I don't think it used annotations at all, but maybe it does now.

When PEP 563 is accepted, there are some tools using runtime type in
annotation, but they are not adopted widely yet.

Yes, that's completely fair.

Samuel