An alternative if you exhaust or don't trust other options, use a foreign data wrapper to access your own custom storage. A single table at the PG level, you can shard the data yourself into 8 bazillion separate stores, in whatever structure suites your read and write operations (maybe reusing an embedded db engine, ordered flat file+log+index, whatever).
However even 8 bazillion FDW's may cause an "overflow" of relationships at the loss of having an efficient storage engine acting more like a traffic cop. In such a case, I would opt to put such logic in the app to directly access the true storage over using FDW's.
I mean one fdw table, which shards internally to 8 bazillion stores on disk. It has the sharding key, can calculate exactly which store(s) need to be hit, and returns the rows and to PostgreSQL it looks like 1 big table with 1.3 trillion rows. And if it doesn't do that in 30ms you get to blame yourself :)