Verify upgrade procedure for PostgreSQL 13 on PG HA installations

Outcome

Upgrades take a while to resolve fully, but they complete successfully.

We decided to isolate the investigation of this slow process to #6664.

For now, upgrading users may experience a few minutes of 500s even after the upgrade is marked complete, but multiple engineers have verified that they do complete successfully, which means our procedure is still correct.

Original Description

We need to be able to upgrade a PG HA installation from PostgreSQL 12.X to 13.X.

The process should be similar to the procedure for upgrading from 11.X to 12.X

Initially, this will be an opt-in upgrade process.

Issue used when adding PG 12: #5497 (closed)