These exact checks are probably too implementation-dependent. Could we just check that the recommendation is, like, higher than detection_ratio * 2 for the first couple of results so that we don't have to update the tests each time we fine-tune some constant by a tiny bit?

This test is just describing how it actually behaves. Is it requirement or implementation detail? Impossible to say without actually having the requirements. I think it acts nicely as documentation of current behavior and is very easy to change if needed.
If we fine-tune some constant and this test fails, it will be very nice feedback in seeing what those constants actually influence and we can then do informed decision about whether we want to change the test or not.

Not a hill I want to die on, but this particular example seems like an overspecified test. Almost to the point where if it breaks, you just adjust it without a second thought, which undermines the value of such test.

We should wrap this in a way that the exception tells the user to install the adaptive-playwright extra. But since this is a private subpackage, maybe it can wait until the adaptive playwirght functionality is made public.