Thanks for your review, @jrfnl. This PR is ready for another check. Below, I'm replying to the points that you raised.

The "header" comment used Safeguard support for PHP 8.0+ tokenization of namespaced "names". is confusing.
These tests are not directly related to PHP 8.0, as on PHPCS 3.x, the "old" tokenization is also used for PHP 8.0 - current, while on PHPCS 4.x, the "PHP 8.0 tokenization" is also used for PHP 7.2 - 7.4.
In my opinion, it would be clearer to call this "Safeguard correct handling of [all types of] namespaced function calls" or "Safeguard against false positives on namespaced function calls".

I pushed commits updating this header. I opted to push one commit per test file to make it possible to combine them with the original commit if the idea is to merge this PR with one commit per changed test file. Happy to help with that after you approve this PR if you want.

All the new tests per sniff use the "same" function name/code. When a sniff is looking for multiple functions, it's never a bad thing to have some variation in the tests.
Example: DateTime/RestrictedFunctions - the namespaced name tests all use the date_default_timezone_set function name, while the sniff also looks for date().

Since you mentioned that those comments are not blocking, I will keep this in mind for future PRs.

For the \target_function() test (FQN call to global function), if the test file in general has enough tests, like the DB/RestrictedFunctions sniff, it would have been perfectly fine to update a few of the pre-existing tests instead of adding a new test for the FQN function call.

I opted to include a new FQN call to a global function test together with the others to make it easier to spot that all possible cases are covered.

A lot of the test files do not contain any tests with non-lowercase function calls to the target functions. Similar to the previous point - if the test file contains sufficient tests, updating a few of these to be non-lowercase (mixed case, uppercase) would not go amiss.

I created a new commit addressing this, and I will pull it in a separate PR once this one is merged.

A lot of the test files also miss tests against false positives for "same name" method calls/constants/properties etc. While not strictly necessary for PHPCS 4.0, still may not be a bad idea to have these tests.

I haven't created yet, but I will try to find time to prepare a separate PR to include those tests that I agree are important.

The // The sniff should start flagging this once it can resolve relative namespaces. comment seen in quite some of the test files is only partially correct.
namespace\target_function() will start to be flagged when in the global namespace, but not when within a namespace.
When namespace and import use tracking is added, we need to make sure both situations are tested (but that's for later, not now).

I opted to add this comment the way it is because those tests are in the global namespace. I agree that when namespace and import use tracking is added, we will need to include more tests.

@rodrigoprimo Could you please rebase the PR to make it mergable ?

Force-pushed to rebase this PR without changes. See #2572 (comment) for more details on the failing PHPStan job.