I was able to repro the reported failure on main, and confirmed this PR fixes it.

I'm not sure adding the tearDown is helpful though.
the uncache context manager uncaches the names both on enter and exit, and perform some checks on the names - two things that the tearDown doesn't perform.
while having the tearDown may prevent some failures (like this one), its existence might indicate that the uncache context manager is not really needed, which is not necessarily true (I don't know if it matters in practice, just noting the behavior differences).

in any case, I also confirmed that just adding the context manager to test_try_registration without the tearDown fixes the issue.

I'm not sure adding the tearDown is helpful though.

Adding this is proposed by @FFY00. And I am neutral about it.

I'm not sure adding the tearDown is helpful though.

I think you are correct, adding both is unnecessary.

tearDown method and util.uncache provides duplicate function. And util.uncache(name) provides more flexibility than the tearDown method.

tearDown here is a safety net. But do we want to expose the problem early or make the system more robust?

I prefer the former since it's a test case. Thus, I will remove this safe net for now.

Thanks @sunmy2019 for the PR, and @brettcannon for merging it 🌮🎉.. I'm working now to backport this PR to: 3.11.
🐍🍒⛏🤖

GH-104345 is a backport of this pull request to the 3.11 branch.