This needs a type hint for the return type.

This should be :py:class: instead of just :class:

Let's call self.validate() here to use the full validation logic, instead of duplicating a part of it.

You should be able to import everything from reviewboard.reviews.models instead of from each individual submodule. So:
from reviewboard.reviews.models import (
  Comment,
  FileAttachmentComment,
  GeneralComment,
  Group,
  ...)

Can you add a "Version Added" to the docstring.

You don't need the \ here, you can do:
* Added handlers for :py:data:`~reviewboard.reviews.signals.
  comment_issue_status_updated` for each concrete comment class.

We could just do
self._handlers[(Review, review_published)] = self._handle_review_published


There's not really a point to make a _review_signal_classes, if you add any class to the list it would always map to the review_published signal in the loop, plus I don't know what other classes you would add other than Review.

While here can you get rid of the Python 2-ism:
super().handle_save(**kwargs)

Let's move this inside the try block so that if an exception happens while invalidating the cache, it gets logged.

We should always use typing in any of our new code. Can you add type hints to this method and every other new method you've added in this change.
You'll also need to add a 

from __future__ import annotations import at the top of this file.

Can we be more specific about what Exception we're expecting to catch? I don't think an Exception would ever be raised here, if there's no associated review request then review_request = review.review_request would just be None (I think).

Same here, can we be more specific about what Exception we're expecting to catch.

I believe you can do
self.assertSpyCalledWith(
    signal_processor.handle_save,
    instance=review_request)


That should check if signal_processor.handle_save has ever been called with the review_request passed as the instance. Same comment applies to the tests below.

ALl the methods here and below need return types.

Arguments need to be on their own line.

Instead of this you can use self.spy_on and kgb.SpyOpReturn to mock this. Same with the tests below.

For dicts we also need to specify the key and value types, like dict[str, str]. Also if this dict is read-only in this method, then we should use Mapping instead of dict.

While you're here can you get rid of the Python 2-ism here.

Can you update the arguments here so that they're each on their own line.
We also prefer doing ... | None instead of Optional[...], but here the Any type also includes the None type (because Any means it can be any type). So you can remove the Optional.

Can you update the arguments here so that they're each on their own line. Also **kwargs and *args don't need type hints. So this should look like
def _handle_review_published(
    self,
    review: Review,
    **kwargs,
) -> None

This should be BaseComment type instead of Any.