Hmm, is it still a good idea to return a string from __class_getitem__, now that we have types.GenericAlias? Admittedly, that's only available from Py3.9 onwards, but it's probably ok to return strings (or anything, really) in Py3.8 and use GenericAlias for everything since.

I will look into the GenericAlias and update this PR.

Rather than doing a version check on each use, in all __class_getitem__ methods, I'd use something like

cdef object _GenericAlias  # only in .pyx files, to store it outside of the module dict
try:
    from types import GenericAlias as _GenericAlias
except ImportError:
    # Python 3.8 - we only need this as return value from "__class_getitem__"
    def _GenericAlias(cls, item):
        return f"{cls.__name__}[{item.__name__}]"

EDIT: In general, I prefer code that prefers the future proof solution and makes the fallback easy to remove. At some point, the fallback will be removed and that works best if it touches little to nothing of the remaining implementation.

I made the change you requested.

Originally, I was trying to follow your "lazy import" code style. But eventually, this is only executed once per annotation when the code gets loaded, so I don't think it makes much difference for performance.