In TeamCity I can bind TC settings to VCS https://confluence.jetbrains.com/display/TCD9/Storing+Project+Settings+in+Version+Control
There was similar request 6 years ago https://resharper-support.jetbrains.com/hc/en-us/community/posts/206039439-Global-resharper-settings?input_string=Feature%20Request%3A%20add%20versioning%20of%20global%20computer%20settings%20as%20it%20did%20in%20TeamCity
Global computer settings is pretty fragile. It would be nice by default store it in internal repository and allow to store it in custom VCS.
I understand that TC has support of many VCSs and just binds features 'VCS' and 'config' together.
Workaround is pretty simple - %AppData%\JetBrains\Shared\vAny move to prefferable VCS, but it is not user friendly, and it is not what comes to mind when you don't want to corrupt settings.
Exporting settings before each modification does not an option too - find a person who does it. It must be safe by default.
Hope we can find preferable solution.