Session data lookup is one select to database that gives 0..1 rows and uses index. In most cases this is not something you need to worry about.
2. Sessions by definition are ephemeral. A database should not be necessary at all, an in-memory cache should suffice.
3. If you really need to distribute session data across multiple nodes, just propagate them asynchronously. Authentication and authorization are semantically idempotent operations. Having to possibly re-auth when making a cross-region request within milliseconds of logging in might be mildly annoying for the user, but consistency isn't a deal breaker here.
What you mean, "if" - you will need that once you are international. You can't afford to verify every http request against a centralized session store when you have users in Australia, US, Europe, Japan etc. You can't beat the speed of light. My point is, replicating revocation lists that are append-only, only a small megabytes, and can be publicly known, is always easier than syncing session databases for a complexity standpoint.
With JWTs, you would only need to replicate your revocation list of the last X hours (X being your JWT default lifetime) and probably be in the megabytes for the total list. Easy to replicate that ever 5-10seconds to all your locations.