If you were on 3.3.12 you’d need to upgrade to Xibo 4.0 first to upgrade MySQL to version 8.0 and then on to 4.4 which uses MySQL 8.4.
To resolve in your current situation, I would stop the db container, take a full backup of shared/db, and then change the MySQL image version number to 8.0 in the docker-compose.yml file and try recreating that container.
You then need to pay careful attention to the section in the 4.4.0 release notes that talks about legacy MySQL password formats.
If MySQL still won’t start, it’s likely you were using MySQL 5.7 without having done the upgrade from 5.6 to 5.7 completely.
You’d need to stop the container again, and complete the MySQL 5.7 upgrade per notes here: