Further insights:

• If the flag for "internet connection allowed" is a singleton, i.e. globally unique, it's not really possible to have the tests run in parallel via pytest-xdist while still allowing some tests to make http requests. If you want to avoid race conditions here by using locks, you basically go back to sequential execution (at least for everything that uses bot HTTPXRequest).
• If we want to set the flag on a per-test/per-fixture basis, we'd have to use unique HTTPXRequest/httpx.AsyncClient/bot/socket objects for each test and figure out a way how to set the flag via markers or similar methods that don't require manual interaction in the tests

These insights are quite a bummer in terms of incorporating the allow-internet-flag into our standard testing suite. Still, I can see a few options:

• provide different fixtures offline_bot & online_bot that can be used. This requires rewriting all tests to use those new fixtures. It also means that it will harder (or impossible?) to check if a *WithoutRequest class uses the online_bot or vice versa and deny that.
• Instead of aiming to fully incorporate this into our standard test suite, we could try to simply run a sanity check every week or so to detect if any test is using the internet even though I should not. For that, we could cut off the internet connection for almost everything and run only the *WithoutRequest & ext tests.

@harshil21 what do you think?

closing in favor of #4454