Progress ... there's something weird going on with the centos postgres package(s).  After a bunch of removes and installs of postgres the engine install succeeded and the engine configuration succeeded.

Now it looks like not all of the postgresql libraries were loaded.

[root@ovirt1 ~]# engine-backup --mode=backup --file=empty-2022-06-12-post-install.bak
Start of engine-backup with mode 'backup'
scope: all
archive file: empty-2022-06-12-post-install.bak
log file: /var/log/ovirt-engine-backup/ovirt-engine-backup-20220612200130.log
psql: /lib64/libpq.so.5: no version information available (required by psql)
psql: /lib64/libpq.so.5: no version information available (required by psql)
psql: /lib64/libpq.so.5: no version information available (required by psql)
Backing up:
psql: /lib64/libpq.so.5: no version information available (required by psql)
psql: /lib64/libpq.so.5: no version information available (required by psql)
psql: /lib64/libpq.so.5: no version information available (required by psql)
Notifying engine
- Files
- Engine database 'engine'
Notifying engine
FATAL: Database engine backup failed

There's a version mismatch between the libpq and the postgresql verson:

[root@ovirt1 ~]# dnf info --installed libpq* postgresql*
Installed Packages
Name         : libpq5
Version      : 14.3
Release      : 42PGDG.rhel8
Architecture : x86_64
Size         : 793 k
Source       : libpq5-14.3-42PGDG.rhel8.src.rpm
Repository   : @System
From repo    : pgdg-common
Summary      : PostgreSQL Client Library
URL          : https://www.postgresql.org/
License      : PostgreSQL
Description  : The libpq5 package provides the essential shared libraries for any
             : PostgreSQL client program or interface. You will need to install this package
             : to use any other PostgreSQL package or any clients that need to connect to a
             : PostgreSQL server.

Name         : postgresql
Version      : 12.11
Release      : 2.module_el8.6.0+1153+eb826827
Architecture : x86_64
Size         : 5.4 M
Source       : postgresql-12.11-2.module_el8.6.0+1153+eb826827.src.rpm
Repository   : @System
From repo    : appstream
Summary      : PostgreSQL client programs
URL          : http://www.postgresql.org/
License      : PostgreSQL
Description  : PostgreSQL is an advanced Object-Relational database management system (DBMS).
             : The base postgresql package contains the client programs that you'll need to
             : access a PostgreSQL DBMS server, as well as HTML documentation for the whole
             : system.  These client programs can be located on the same machine as the
             : PostgreSQL server, or on a remote machine that accesses a PostgreSQL server
             : over a network connection.  The PostgreSQL server can be found in the
             : postgresql-server sub-package.