On reviewing the log from engine-setup:

2022-06-12 23:27:29,507-0400 DEBUG otopi.context context._executeMethod:127 Stage setup METHOD otopi.plugins.ovirt_engine_common.ovirt_engine.db.connection.Plugin._setup
2022-06-12 23:27:29,510-0400 DEBUG otopi.ovirt_engine_setup.engine_common.database database.execute:234 Database: 'None', Statement: '
                    select 1
                ', args: {}
2022-06-12 23:27:29,510-0400 DEBUG otopi.ovirt_engine_setup.engine_common.database database.execute:239 Creating own connection
2022-06-12 23:27:29,638-0400 DEBUG otopi.ovirt_engine_setup.engine_common.database database.tryDatabaseConnect:394 Connection failed
Traceback (most recent call last):
  File "/usr/share/ovirt-engine/setup/ovirt_engine_setup/engine_common/database.py", line 390, in tryDatabaseConnect
    transaction=False,
  File "/usr/share/ovirt-engine/setup/ovirt_engine_setup/engine_common/database.py", line 248, in execute
    database=database,
  File "/usr/share/ovirt-engine/setup/ovirt_engine_setup/engine_common/database.py", line 181, in connect
    sslmode=sslmode,
  File "/usr/lib64/python3.6/site-packages/psycopg2/__init__.py", line 127, in connect
    conn = _connect(dsn, connection_factory=connection_factory, **kwasync)
psycopg2.OperationalError: FATAL:  password authentication failed for user "engine"
FATAL:  password authentication failed for user "engine"

I am able to log in to the database with the engine user credentials.

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

engine=> \q

Question: Is the engine-setup possibly trying to run with no password??