Currently _xxsubinterpreters.run_string() fails if the interpreter has other threads running, e.g. subthreads created by a previous run_string() call. This should be fixed to allow other threads to be running.

Linked PRs

• gh-105716: Support Background Threads in Subinterpreters Consistently #109921
• [3.12] gh-105716: Support Background Threads in Subinterpreters Consistently (gh-109921) #110707
• [3.12] gh-105716: Fix "Refleak" Failures in test_interpreters #112500
• gh-105716: Update interp->threads.main After Fork #117049
• gh-105716: Fix _PyInterpreterState_IsRunningMain() For Embedders #117140