[clangd] Fix race in Global CDB shutdown

I believe the atomic write can be reordered after the notify, and that
seems to be happening on mac m1: http://45.33.8.238/macm1/2654/step_8.txt
In practice maybe seq_cst is enough? But no reason not to lock here.

https://bugs.llvm.org/show_bug.cgi?id=48998
(cherry picked from commit 6ac3fd97)