Hello. If i make a full backup of my current HA supervised installation and then restore it on newly installed HAOS, will it work without additional tweaks? Same machine, same port for Zigbee dongle. Will it also store all the historical data from recorder (MariaDB in use)
Yes.
To be sure the MariaDB add-on is backed up correctly stop the add-on before creating the full backup.
This will cause quite a few errors in your logs as the DB cant be written to but the backup will have a better chance of working without database corruption.