Update:

I scanned the centos libraries, and the lowest version of postgres that had consistent package versions was 13. There was no libpq at the version 12 level in the centos RPM library.

I performed the manual installation process for the postgresql database at the Initializing the PostgreSQL Database at https://www.ovirt.org/documentation/installing_ovirt_as_a_standalone_manager_with_local_databases/ , using version 13 instead of version 12.

On completion of database configuration, engine-setup reports:

[root@ovirt1 engine.conf.d]# engine-setup
[ INFO  ] Stage: Initializing
[ INFO  ] Stage: Environment setup
          Configuration files: /etc/ovirt-engine-setup.conf.d/10-packaging-jboss.conf, /etc/ovirt-engine-setup.conf.d/10-packaging.conf, /etc/ovirt-engine-setup.conf.d/20-setup-ovirt-post.conf
          Log file: /var/log/ovirt-engine/setup/ovirt-engine-setup-20220612221218-ogmuo6.log
          Version: otopi-1.9.6 (otopi-1.9.6-1.el8)
[ ERROR ] Failed to execute stage 'Environment setup': Cannot connect to Engine database using existing credentials: engine@localhost:5432
[ INFO  ] Stage: Clean up
          Log file is located at /var/log/ovirt-engine/setup/ovirt-engine-setup-20220612221218-ogmuo6.log
[ INFO  ] Generating answer file '/var/lib/ovirt-engine/setup/answers/20220612221225-setup.conf'
[ INFO  ] Stage: Pre-termination
[ INFO  ] Stage: Termination
[ ERROR ] Execution of setup failed

Attempting to connect via psql:

[root@ovirt1 engine.conf.d]# psql engine@localhost:5432
psql: error: FATAL:  database "engine@localhost:5432" does not exist

[root@ovirt1 engine.conf.d]# psql -h localhost -U engine
psql: error: FATAL:  Ident authentication failed for user "engine"

[root@ovirt1 engine.conf.d]# psql -h 127.0.0.1 -U engine
Password for user engine:
psql (13.7)
Type "help" for help.

engine=>