Never mind lol, you can upgrade it, you just need to specify. Normally or at least until now it wasn’t needed:
root@gitlab:~# gitlab-ctl pg-upgrade -V 16
Checking for an omnibus managed postgresql: OK
Checking if postgresql['version'] is set: OK
Checking if we already upgraded: NOT OK
Checking for a newer version of PostgreSQL to install: OK
Upgrading PostgreSQL to 16.4
Checking for previous failed upgrade attempts: NOT OK
Checking if disk for directory /var/opt/gitlab/postgresql/data has enough free space for PostgreSQL upgrade: OK
so you can upgrade to 16.
And all done 
root@gitlab:~# gitlab-psql --version
psql (PostgreSQL) 16.4
Will do some more testing, but hopefully it’s working fine, so you may want to make a backup of your server and then try the same as my previous post.