The question is too broad. For sure from time to time caches become different (either added more fields, props, even changing the database structure and database itself perhaps).
AFAIK, there is no callback à la
virtual void OnCacheCompatibility(long previousVer, long currentVer, ISomeCacheDatabaseInterfaceDelegate* delegate) = 0;
to be invoked on CEF startup.
Also, the cache path contains multiple things (stored files, cookies, user prefs), each one probably with its own compatibility logic.
For sure there is a mechanism that does the upgrade in Chromium, but I don't think is something exposed from content/ or public/.
Most likely you need to do it from the app somehow.
Assuming you want to modify Chromium yourself, I'd start from
here.