`trace` function is cleared after `RecursionError` is fired

Bug report

Bug description:

I'm using coverage and pytest-cov in CI to measure the line coverage of the unittests. It is achieved by registering a trace function with sys.settrace.

However, after binsecting my unittests, I found that when a RecursionError is raised, the system trace function will be cleared. That will cause a warning emitted by coverage:

~/Projects/cpython/venv/lib/python3.15t/site-packages/coverage/pytracer.py:355: CoverageWarning: Trace function changed, data is likely wrong: None != <bound method PyTracer._trace of <PyTracer at 0x200021dcc20: 2076 data points in 11 files>> (trace-changed)
  self.warn(

Reproducible code:

import sys


def tracer(*args, **kwargs):
    pass


def factorial(n: int) -> int:
    """Calculate the factorial of a number."""
    if n <= 1:
        return 1
    return n * factorial(n - 1)


sys.settrace(tracer)
assert sys.gettrace() is tracer

sys.setrecursionlimit(64)
assert sys.gettrace() is tracer

try:
    _ = factorial(100)
except RecursionError:
    pass

assert sys.gettrace() is None

REPL Output:

# Add a code block here, if required
$ python3                      
Python 3.13.3 (main, Apr  8 2025, 13:54:08) [Clang 16.0.0 (clang-1600.0.26.6)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import sys
>>> def tracer(*args, **kwargs):
...     pass
... 
>>> def factorial(n):
...     if n <= 1:
...         return 1
...     return n * factorial(n - 1)
...     
>>> sys.settrace(tracer)
>>> sys.gettrace() is tracer
True
>>> sys.setrecursionlimit(64)
>>> _ = factorial(100)
Traceback (most recent call last):
  File "<python-input-6>", line 1, in <module>
    _ = factorial(100)
  File "<python-input-2>", line 4, in factorial
    return n * factorial(n - 1)
               ~~~~~~~~^^^^^^^
  File "<python-input-2>", line 4, in factorial
    return n * factorial(n - 1)
               ~~~~~~~~^^^^^^^
  File "<python-input-2>", line 4, in factorial
    return n * factorial(n - 1)
               ~~~~~~~~^^^^^^^
  [Previous line repeated 51 more times]
  File "<python-input-2>", line 1, in factorial
    def factorial(n):
    
RecursionError: maximum recursion depth exceeded
>>> sys.gettrace() is None
True

CPython versions tested on:

CPython main branch

Operating systems tested on:

macOS

Run the supplied reproducer and inspect the behavior of sys.settrace, sys.gettrace, and RecursionError around the recursive factorial call. Trace the CPython implementation paths involved in recursion-limit handling and tracing; done means the registered trace function remains available after the RecursionError, with regression coverage for the reproducer.