subprocess.run keeps waiting after the process termination.
This happens when stdout or stderr is redirected, and the started process pass that stream to a background process.

Reproduction:
Create count.sh

function count {
    for i in 1 2 3 4 5;
    do
        sleep 1
        echo "$i" >&2
    done
}
count &
echo "Done" >&2

Reproduce with:

import subprocess
subprocess.run(["/bin/bash", "./count.sh"], stdout=subprocess.PIPE, timeout=1)

Result:
subprocess.TimeoutExpired: Command '['/bin/bash', './count.sh']' timed out after 1 seconds
This is not correct as the subprocess has terminated and produces a return code.
The expected behavior for run is to return as soon as the instanciated terminates, regardless of the streams lifecycles.

Variants:
Calling subprocess.run(["/bin/bash", "./count.sh"], timeout=1) works as expected, that is to say run returns immediately.

Environment:

Python 3.8.9:

• CPython versions tested on:
• Operating system MacOs, Linux