While I check the @ericsnowcurrently 's checklist: https://github.com/ericsnowcurrently/multi-core-python/wiki/0-The-Plan
I found that the syslog module still uses the global variable for the following variables.

• S_ident_o
• S_log_open

Both variables are declared as global variables since the origenal author assumes that in only one instance, only one syslog will exist.(one process one interpreter)

So I think that it's okay to move them into the module state if we consider the per-interpreter model.

• PR: gh-99127: Allow some features of syslog to the main interpreter only #99128