Setup from Zero
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It's the mysql.h, probably.
The 'do the secure installation' step that is now recommended does something that changes the standard permissions that tinymux expects when it comes time to configure it.
I know I managed to fix it once. I do not for the life of me remember how, but it wasn't any of the things recommended on the thread to fix the mysql.h issue, because none of those worked for me at all.
It may have been some kind of worst practice hail mary I yanked out of my ass, so I don't recall, unfortunately, what it was. It was a permissions issue, that much I do remember. Whether it involved changing the permissions on the directory where the file was housed or the file itself, and what I ended up changing them to, unfortunately, I do not remember.
I know that isn't much help, but maybe with that information some of the people who actually know what they're doing can help narrow it down.
ETA: For the tech people: If this is a digitalocean install, mysql.h is there, and it is installed. The permissions are just locked down in such a way that tinymux can't access it to use it to do anything -- which may be only after the 'mysql_secure_installation' step, but even if you did this after setting up tinymux you'd run into the same issue later -- so tinymux acts like it isn't there because it can't see or use it.
ETA2: Mediawiki 1.30.0, the current version, is fussy and different in some new and interesting ways. Be advised if you're using code from an earlier iteration or planning to import. Apparently a lot of stuff deprecated between versions 29 and 30 and you will probably need to tweak your stuff. Depending on how much you fuss with things, this may be no big deal.
(I know I found the stuff they're starting to add in so egregiously annoying I gave up on using Vector entirely and started building a new skin during the time I can't really do anything else productive (while this comp is on its last teetering legs and we settle in for the long wait for its replacement).)