[3.13] gh-120974: Make asyncio `swap_current_task` safe in free-threaded build (GH-122317) (#122612)

gh-120974: Make asyncio `swap_current_task` safe in free-threaded build (GH-122317)

* gh-120974: Make asyncio `swap_current_task` safe in free-threaded build
(cherry picked from commit b5e6fb39a246bf7ee470d58632cdf588bb9d0298)

Co-authored-by: Sam Gross <colesbury@gmail.com>