Do I just do that by clicking on the + New Account button, please?

Yes. Note, Gmail uses OAuth authentication. You need to allow cookies in Thunderbird for the OAuth authentication to succeed.

I'd hate to lose access to my BT mail by doing that.

You won't.

Having said that, it is always a good idea to create backups of your Thunderbird profile on a regular basis. https://support.mozilla.org/en-US/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

Hi Christ1 -

That was v helpful and it worked for me first time. A follow-up question - is it possible to add different background colours to the three inbox folders I have now, please? I can change the colours of mail I send (via Composition), but not mail I get. I've found an old (2020) Add Colors Add-On as part of the Unified Folders page but it's no longer supported and Firefox doesn't verify it.

is it possible to add different background colours to the three inbox folders I have now, please?

Your follow-up question is unrelated to your original problem. Best practice in this forum is one problem per topic. Therefore please start a new topic for the new question. https://support.mozilla.org/questions/new