wordpress versions compability

Your versions are not that far off. Do you really mean MariaDB below v10? v10.* would be better (10.4.12 latest stable). You might start there. Before doing so on the production site, I’d clone it to a staging or localhost site. Localhost with a hosts file entry for the domain allows you to use the DB unchanged, though you could not then access the production site on that machine.

If production content is actively updated, avoid making DB changes to your clone to avoid sync issues. The goal would be to get all localhost code working well on the latest versions, not to fiddle with DB content. Update everything to the latest available and deal with any fallout. Address the most egregious issues first, like fatal errors (duh!). Then warnings and notices. Don’t worry too much about pagespeed for now. Get everything working on the latest versions without logging any errors. If everything works on PHP 7.1 it shouldn’t be too bad.

Some people have reported sporadic issues with WP 5.3, but there are millions using it without issue. Issues are usually due to outdated add-ons or odd server configurations.

WP updates to the DB will only affect its own schema, they do not affect the DB engine version. The DB engine version is outside of WP, just as PHP, Apache and the O/S versions would be independent of WP updates. Your DB schema is very nearly up to date by virtue of WP 5.2. That is unrelated to the MariaDB version. WP updates its schema during regular version updates, but updating MariaDB is up to you or whom ever the sysadmin is.

Whether you setup a localhost test site or not depends in part on whether you want to keep the production site up or not. If updates cause fatal errors, the site will be down until you can resolve the errors. Even if not fatal, it may not work correctly right after an update. If having the site go down or not work right for a time is acceptable, you can just update the site directly. I happen to prefer working on localhost anyway. For any major work on a site, I think it’s worth cloning locally.

Testing site functionality on a variety of devices could be an issue on localhost. It depends on how your LAN is setup and if the devices are tied into it. Even if complete testing locally is not possible, at least you can get the bulk of it working in browsers and mobile emulators running on your work station. Final testing could be postponed until the site is live.

Since you are not completely confident of your sysadmin skills, I think that is all the more reason to work on a local copy. Much less pressure to get it right (and no one will see the mistakes you make along the way 🙂 ) This does add to the tasks you need to accomplish if a localhost installation is not already in place. I think it’s worth doing anyway. TBH, the updates should go fairly well. I don’t really anticipate any problems. But there is always that chance. I’d rather find out on a test installation than a client’s production site. If you’d rather not mess with localhost, it’ll probably be fine.

BTW, the auto updates are only applied for minor updates. Major point updates like 5.x always require manually starting the process. Minor updates are often security patches which you shouldn’t want to postpone. For most users, minor updates happen without a hitch.

Some hosts really drag their feet with version updates. In the case of DB versions, I’d fully expect an otherwise up to date WP installation to work fine on an older MariaDB. End of life PHP versions would be much more concerning.

5.5 isn’t as bad as it sounds, MariaDB versions jumped from 5.5 to 10.0.

Warning: once you get comfortable working on WP locally, being forced to do any significant development on a remote server becomes rather unpleasant 🙂