If you send from a non-gmail account, but use the gmail smtp server, gmail will replace the non-gmail address with the gmail address associated with the smtp. Recipients will see the gmail account as the sender. To avoid this, use the smtp for the non-gmail account, or add the non-gmail account to the gmail account in gmail website settings, Account & Import, Send mail as.

Fabulous, thanks sfhowes! I added the desired address to gmail as an alias, now it works from Thunderbird. Still, it is strange that this was not previously required; I wonder, did Google recently change something?

In gmail I also selected "Reply from the same address the message was sent to", since it was set to "Always reply from default address", even though it says that can be changed when sending (which did not seem to work). Perhaps that is all that was required rather than adding the alias address, yet I have done both to be certain.

I think the Google policy of swapping in the gmail address without notice has been in place for years, and it's especially useful for ISP accounts that don't have secure smtp servers. I don't know what has changed at the gmail end, although they do seem to enforce or prefer OAuth2 authentication now instead of 'normal password'.

Not sure about the 'Always reply...' setting, but some simple tests should reveal the effect. It may work on the gmail website but not through mail clients. Adding the address as a sender does work with TB.