Hello,
after updating the external engine from CentOS 8.4 and 4.4.8 to Rocky Linux 8.5 and 4.4.9 as outlined here:
https://lists.ovirt.org/archives/list/users@ovirt.org/message/YUDJRC22SQPAPAIURQIVSEMGITDRQOOM/
I went further and updated also the hosts.
Environment is with an external engine and 3 CentOS Linux 8.4 hosts in 4.4.8 with iSCSI storage domain.

Preliminarily I upgraded the engine to 4.4.10 (not yet the just released async) without problems.
Then, one host at a time:

. put host into maintenance from web admin UI
Management --> Maintenance

. In a terminal f host set proxy for my environment needs
export https_proxy=http://my_proxy:my_proxy_port
export http_proxy=http://my_proxy:my_proxy_port (not sure if this necessary...)

. in the same terminal execute migration script
./migrate2rocky.sh -r

. executed Management --> SSH Management --> SSH Restart from web admin ui
the host comes on in maintenance mode

. selected Installation --> Check for Upgrade but the host is detected as already update

. for further security and to be sure that all upgrade steps are applied I executed
Installation --> Reinstall
I deselected
- activate host after install
- reboot host after install
It went ok so

. executed Management --> SSH Management --> SSH Restart from web admin ui
the host comes on in maintenance mode

. Management --> Activate

. Empty another host moving its VMs to the just updated host and continue in the same way, also electing as new SPM the updated host

All went smoothly and without VMs disruption.
Let's see how it goes next days with the light workload I have on this testing environment.
Currently the async 1 of 4.4.10 is not catched up by engine-upgrade-check command.. I'm going to retry applying again during the next few days.

Gianluca