[3.13] gh-117657: Fix race involving immortalizing objects (GH-119927) (#120005)

The free-threaded build currently immortalizes objects that use deferred
reference counting (see gh-117783). This typically happens once the
first non-main thread is created, but the behavior can be suppressed for
tests, in subinterpreters, or during a compile() call.

This fixes a race condition involving the tracking of whether the
behavior is suppressed.

(cherry picked from commit 47fb4327b5c405da6df066dcaa01b7c1aefab313)