I don't think any of the extensions actually provides the type of auto-tuning / balancing you're asking for, actually. For example pg_partman helps with setting

I don't think any of the extensions actually provides the type of auto-tuning / balancing you're asking for, actually. For example pg_partman helps with setting up some partitioning schemes (by time, by ID), but does not rebalance it later (e.g. to split a hot or unexpectedly large partition). It probably provides more convenient interface to do that, but it's still up to the DBA to do it. I'm sure this is one of the things people on pgsql-hackers will be talking about, but I wouldn't hold my breath for it to get into PG12. I do expect this to emerge in an extension first, and then getting the most useful bits into core (either in the form of built-in features, or hooks allowing extensions to be smarter).