One of the upgrade steps from Debian Buster to Debian Bullseye for servers running PostgreSQL should be the upgrade from version 11 to 13 (or higher).
First install the updated packages:
apt -y install postgresql-13 postgresql-client-13
The upgrade process below assumes there is only the single instance/cluster named main (the default).
Before running any of the below commands make sure you have a current backup.
sudo pg_dropcluster --stop 13 main
pg_upgradecluster to import the version 11 data to version 13:sudo pg_upgradecluster 11 main
sudo pg_dropcluster 11 main
sudo apt --purge remove postgresql-11 postgresql-client-11
sudo apt --purge autoremove