I have a feeling the problem is caused by the way the board, clone and STK are installed. The Instalatron is something designed by your host and only they know how it's configured. The problem you have with the bb_tables being recognised as extra tables is because the STK does not expect those tables being in the database, probably because it expects a different table prefix. (years ago when I had used the STK, it was on a copy of the live database, but with each table replicated using a different prefix; so the STK message was correct but caused no problems).
In this case using the Installatron seems to have unexpected results, and is a reason why support for those installations is not (able to be) given.
My suggestion: (first take a backup of everything) install a new phpBB 3.0.14 as recommended by phpBB, import your current database into it. Verify that it is in working order. Take a full backup. And then try to upgrade as per instructions from phpBB.
Should you by any stroke of luck do know how to work with a personal webserver (or are willing to try), have a look at USBWebserver (use https://www.usbwebserver.net/webserver/
version 8.6). It will allow upgrading to 3.2.4 (of that I'm certain, done it 10+ times) on your PC after which you can transfer back to online.