Postgres like MySQL/MariaDB in that DB users are granted privs. There is also a host setting in non Postgres DB servers. Now I know those shouldn't have changed in Postgres as you are just upgrading the code, but ... what of privs and host settings for the new Moodle DB user, DB, etc. instance?
Also, believe Moodle recommends a path for upgrades from lower versions to highest version.
A 2.6.x, for example would need to go to a 2.7.highest first and then one could march it to 3.2.highest.
Probably many changes between 2.6.x and 3.2.highest.
Have seen errors reported in Moodle that were not quite accurate ... a little misleading. So are there Postgres logs that you could check?
'spirit of sharing', Ken