FWIW I just found this article suggesting I can drag & drop files locally (in Thunderbird) from an older POP account to a newly created IMAP one:-

https://support.mozilla.org/en-US/kb/switch-pop-imap-account

But that's likely to take days!! And AFAICT from experimenting here, it only works for received emails. Sent emails didn't seem copyable when I tried it here.

Surely there's a way to just change the Account Type?

Sorry, POP and IMAP are different and a separate account would be needed. However, it is possible to upload both received and sent messages, but it can be problematic if you have a lot of messages. A compromise might be to migrate your POP message folders to Local Folders and manage them from there, using the IMAP account going forward.

Many thanks david, I'll give some thought to your Local Folders suggestion.

BTW, am I right in thinkng that IMAP saves messages remotely, rather than on my local machine? I'm not quite sure if that'd be a blessing or a curse :-)

IMAP keeps all messages on the server. Many link that as it allows interaction with account from multiple locations and from phone.

Sorry if this seems like a dumb question david, but for an IMAP account, whereabouts is the server where my emails are stored? I know my email provider has its server but AFAIK it only keeps things for around 30 days or so.

This may be something to check with email provider. My experience with email provider is that, for IMAP account, the user is allocated an amount of space and can keep messages there as long as desired. However, the email provider might have an expiration time for trash at 30 days as a courtesy to user.