OK, in partial answer to my own question, random thrashing around on forums suggests
$ sudo apt-get install libmysqlclient-dev
will then allow mysql2 gem to install (whatever that is) - ignoring the warning about not doing this as root.
Getting past that and to the next step - typing
$ bundle exec rails db:drop
gives another error::::
bundler: failed to load command: rails (/usr/local/bin/rails)
Gem::Exception: can’t find executable rails for gem railties. railties is not currently included in the bundle, perhaps you meant to add it to your Gemfile?
Checking in /usr/local/bin/ and I can see a file named ‘rails’ is definitely there.
Typing $ sudo gem or $ gem install rails or $ sudo gem install rails does not help (per various suggestions stumbled across for this error).
Have even gone back and installed Ruby on Rails from scratch to try and ensure all normal dependencies are present How To Install Ruby on Rails with rbenv on Ubuntu 18.04 | DigitalOcean -and no improvement - whether I use version 2.51 or 2.61.
Well out of my depth here…