Glad to hear that you got it up and running again.

Firstly, what you've done sounds a bit messy, but if it works, then IMO it's fine to keep going. At some point you are going to need to migrate/upgrade, so personally, I'd be looking at focusing on that, rather than worrying too much about this server.

Essentially what you've done is installed a newer version of Adminer (from Debian 10/Buster; a much newer version of Debian than 8/Jessie - what v14.x was based on). Generally that sort of thing is frowned on and considered to be a FrankenDebian. However, having a closer look at this specific scenario, with a newer version of PHP, I suspect that it's unlikely to cause any issue; especially consdiering that you installed the deb file directly (rather than adding the newer repo and installing with apt - which would risk pulling in other packages). As you can see the Adminer package only depends on PHP packages so the chances of just Adminer causing any issues is slim.

As to trying to work out what happened, you note that you have installed a newer version of PHP. If you did that prior to installing this newer version of Adminer, then that may have been why? The old Adminer would have depended on PHP 5.6 packages (named php5...), so if you uninstalled any of those, then you probably inadvertently uninstalled Adminer while you were doing that.

You may be able to prove (or disprove) my theory via the apt logs. I suggest trying something like this for starters:

zgrep adminer /var/log/apt/*

Hopefully that will output at least one line (probably multiple lines) in this format:

/var/log/apt/FILENAME.log.XX.gz: MESSAGE_CONTAINING adminer ...

Eg. here's a real line that demonstrates an example line from a search of log file (zgrep acpid /var/log/apt/*) on a server I have handy.

/var/log/apt/term.log.11.gz:Removing acpid (1:2.0.28-1+b1) ...

The first part (before the first ':') is the filename where the match occurs.

If that gives too many results, then you could try searching for the explicit term "Removing adminer":

zgrep "Removing adminer"r /var/log/apt/*

Regardless, if you wish to review the file manually, I suggest use of 'zcat' with 'more'. More is a pager, so you can scroll through the file contents use 'space' to scroll a full page, 'enter' to scroll line by line.

zcat /var/log/apt/term.log.11.gz | more

FWIW you can use 'more' to search for the desired term ('adminer' in my example below - but as per zgrep example above, you can tweak it using more text within the previous search to be more precise). You can do it interactively by typing '\search term' (after running the above command, without the quotes). Or you can add it to the end of the more command as noted below. Note that in 'more', the search term does not need to be quoted but is case sensitive. Some special characters (e.g. '/') may need to be escaped (e.g. '\/'). So as an example, to search for "Removing adminer":

 zcat /var/log/apt/term.log.11.gz | more +/Removing adminer

As to migrating, I suggest that you do a dry run with TKLBAM (i.e. restore a backup to a new v16.x server running as a VM). If you just do that to a test VM, then worst case, it will completely fail and you can trash the VM and start again... You can work through any issues and/or develop a workflow for the migration with no pressure (taking careful notes as you go so you can recreate your steps later when you do it for real). If you hit any hurdles and/or want any suggestions and advice with issues you may hit, please feel free to post.