The
changelog on your site indicates phpBB 3.2.0, and
your prosilver style version agrees.
That does still mean your phpBB version is only compatible
up to PHP 7.1, and will have some issues if your host is now running PHP 7.2.x or later. Which they presumably would have chosen a later version; but we don't actually know what version they moved you to. Your NGINX web server doesn't give us any hints as to what PHP version is currently in effect.
However, the full-stop issue you're hitting right now is something more specific, and is something which phpBB 3.2.0 actually can handle. Your phpBB config.php is apparently still specifying the
mysql
interface, which was deprecated but still usable after PHP 5.5.0, but became completely removed in PHP 7.0 and later.
So this config.php statement has been working for you just fine, until your host finally switched you from a pre-PHP 7.0 version to any post-PHP 7.0 version, at which point the
mysql
interface no longer exists.
Make a backup copy of your current config.php, and then edit the config.php to now specify
mysqli
instead of
mysql
for the dbms driver line in the config.php. Yes it's almost identical, except for the "i" you see at the end.
You should also go ahead and delete the /forum/cache/production/ folder too, to manually clear the phpBB cache after making this change. Just delete the "production" subfolder including all the files it contains using FTP or other file manager for your site, and don't worry when phpBB probably immediately re-creates the "production" sub-folder, which is normal.
After making these changes, if this restores the SQL connectivity for phpBB on your site, you will then only have "the problems we would expect a phpBB 3.2.0 board to have" if your host has moved you to PHP 7.2.0 or later, which is beyond the PHP versions that phpBB 3.2.0 supported. But those issues are mostly "just PHP warnings", and the board may work sufficiently now to allow you to get logged in to phpBB ACP.
From there you can use the PHP Information section in the phpBB ACP there to see what PHP version your host has actually moved you to. If it happens to be PHP 7.0.x or PHP 7.1.x, you may actually be fine -- for now -- and gives you more time to plan your upgrade. Which as KevC said, sooner or later will become necessary, regardless.