[3.9] GH-100892: Fix race in clearing `threading.local` (GH-100922) (#100939)

[3.9] GH-100892: Fix race in clearing `threading.local` (GH-100922) (#100939)

[3.9] [3.10] GH-100892: Fix race in clearing `threading.local` (GH-100922).
(cherry picked from commit 762745a124cbc297cf2fe6f3ec9ca1840bb2e873)

Co-authored-by: Kumar Aditya <59607654+kumaraditya303@users.noreply.github.com>.
(cherry picked from commit 683e9fe30ecd024f5508b2a33316752870100a96)

Co-authored-by: Kumar Aditya <59607654+kumaraditya303@users.noreply.github.com>