As of 3.12 `_lsprof` no longer calls `_PyEval_SetProfile` making `sys.getprofile()` useless with `cProfile`

Bug report

Bug description:

Starting in 3.12 with the addition of sys.monitoring, _lsprof, specifically in profiler_enable, no longer calls _PyEval_SetProfile.

Very specifically, this impacts previous functionality where python -m cProfile -m whatever would result in sys.setprofile() being called, and subsequently the whatever module could access the profiler object via sys.getprofile()

To my knowledge this is now completely impossible as sys.monitoring provides no meaningful way to access the profiler object.

In my particular use case, profiling could be enabled within the application, or if python -m cProfile was used, the existing profiler could be used allowing profiling to happen earlier than the enablement point of cProfile within the application.

Something to the effect of:

p = sys.getprofile()
if p is None:
    p = cProfile.Profile()
    p.enable()

CPython versions tested on:

3.13

Operating systems tested on:

Linux

Start by tracing _lsprof's profiler_enable behavior and its relationship to _PyEval_SetProfile, then compare the 3.11 and 3.12 behavior of python -m cProfile -m whatever. Check how sys.getprofile(), cProfile, and sys.monitoring interact; done means the intended profiler object remains accessible without breaking the 3.12+ monitoring design.