Failure during the print of select.select output with unblocking sys.stdin

Bug report

Bug description:

This code terminates with error messages after several loop iterations:

import sys
import os
import select

os.set_blocking(sys.stdin.fileno(), False)

while True:
    print('>')
    ready = select.select([sys.stdin, ], [], [], 0.0)[0]
    print(f'< ready={ready}')

$ python3.11 stdin-nonblocking-bug-report.py
<... skip many iterations ...>
< ready=[]
>
< ready=[]
>
< ready=[]
Traceback (most recent call last):
Exception ignored in: <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>
Exception ignored in sys.unraisablehook: <built-in function unraisablehook>

$ echo $?
120

The failure occurs in print(f'< ready={ready}').

Python-3.11
FreeBSD 14.1

CPython versions tested on:

3.11

Operating systems tested on:

Other

Start with the provided reproducer that sets sys.stdin nonblocking and repeatedly calls select.select before printing. Reproduce the failure on Python 3.11 with FreeBSD 14.1, then trace the stdout print and shutdown path to identify the cause. Done means the loop no longer produces the reported unraisable I/O error under the stated conditions.