sys.setrecursionlimit docs are incorrect in 3.12 and 3.13

[dimpase]

Since 3.12, sys.setrecursionlimit does not control the recursion limit of the C stack (it's hardcoded in Py_C_RECURSION_LIMIT, due to #91079), while the 3.13 docs say

Set the maximum depth of the Python interpreter stack to limit. 
This limit prevents infinite recursion from causing an overflow of the C stack and crashing Python.

The fallout can be seen in #112215 (basically, any code that uses lru_cache in combination with sys.setrecursionlimit is potentially, or actually, broken in 3.12, while still working in 3.11) or in #107263 (which was papered over with an increase of Py_C_RECURSION_LIMIT, not really fixed).

This is an obvious change of behaviour, as code working in 3.11 can easily be broken in 3.12, as found in #112215

import sys
sys.setrecursionlimit(1001)
from functools import cache
@cache
def fib(n):
    if n<1: return 0
    if n==1: return 1
    return fib(n-1) + fib(n-2)

print(fib(500))

$ python3.11 <fib.py 
139423224561697880139724382870407283950070256587697307264108962948325571622863290691557658876222521294125
$ python3.12 <fib.py 
Traceback (most recent call last):
  File "<stdin>", line 15, in <module>
  File "<stdin>", line 13, in fib
  File "<stdin>", line 13, in fib
  File "<stdin>", line 13, in fib
  [Previous line repeated 496 more times]
RecursionError: maximum recursion depth exceeded

Such changes should carry a warning in the documentation.

Potentially, any recursive Python code combining C recursion (in a module, e.g. lru_cache, via @lru_cache decorator) with increased (beyond the hardcoded Py_C_RECURSION_LIMIT) sys.setrecursionlimit is bound to be broken in 3.12.

I believe the whole hardcoding of Py_C_RECURSION_LIMIT has to be fixed (perhaps with a separate API provided to change it), as it's a regression and an incompatible change of code behaviour, but meanwhile the docs have to reflect the reality.

[Jiehong]

I confirm this breaks some code out there.

In particular, we are unable to move from python 3.11 to anything higher, since we can no longer pickle.dump our objects, even if sys.setrecursionlimit is called beforehand for example.