I personally moved from SQLite to a B-Tree based key-value store, and most requests can be serviced in ~500us (that is microseconds). I don't mean a request to the database: I mean a request from the client side that queries the database and fetches multiple objects from it. In my SQLite setup, the same kind of query would take 10ms (that is 20x the time) even _with_ accelerator structures that minimize hits to the DB.
But you can always scale up vertically. You can pay $240/mo for 8 vCPUs with 32GB of RAM. Much cheaper than you would pay for an elastic cloud cluster.
500us is slow. This kind of performance does not remotely obsolete an LRU cache (main memory access is ~5000X faster).
500us is essentially intra-datacenter latency. Obviously your data is in memory on the B-Tree server as there is no room in this budget for disk IO. Postgres will perform just as well if data is in memory hitting a hash index (even B-Tree probably). I don't think the B-Tree key-value store you mention is adding much. Use Redis or even just Postgres.
SQLite?
If yes, then I dont really believe that you can have 20k concurrent users where significant part goes to db, not cache.
But Ive been messing with just 1 vCore, so.