Use native parse_type_string()

[ilevkivskyi]

Fixes #21515

I also fix one remainder from Python 2 age where we accepted bytes literals as forward references.
cc @JukkaL

[ilevkivskyi]

Btw note I am not touching parse_type_comment() in stubgenc.py yet. That one is a bit trickier, and will be probably better handled later by people more familiar with stubgen.

[github-actions]

According to mypy_primer, this change doesn't affect type check results on a corpus of open source code. ✅

[JukkaL]

I guess this was the last use case of the legacy parser when type checking while using the new parser, nice!