OK – I fixed part of the problem by logging into my Gmail webmail account and seeing I had mistakenly left the option “Always reply from default address” checked instead of “Reply from the same address the message was sent to.”
Now, however, when I reply to a message sent to an alias, the From address is my main user account, not the alias the message was sent to.
There is no user “firstname.lastname@example.org” at Google though – it’s only an alias – and none of the passwords I try (the one for Google Workplace, the old G Suite Legacy or the primary user Gmail account) work.
I called Apple and they said to delete the gmail account in Mail and recreate it, which didn’t change anything.
This was asked in a slightly different way in another thread, and, since the iOS mail app doesn’t allow you to list alias addresses for Gmail or Google Workspace accounts anymore, there are only two ways really:
Use the Gmail app
Try the method in the Dan Moren article link in the comment I linked above. The instructions are at the end of the Moren article. (Basically, it’s add another IMAP account and add the aliases to that account.)
Thank you very much for the tips, especially the Dan Moren article, which indirectly led me to the solution.
I am using macOS and POP, which he includes in his comments, and although I didn’t use his method of editing the Email address field in Mail > Preferences > Accounts > Account Information, I realized from what he was saying that in Accounts > Server Settings > Outgoing Mail Server (SMTP) > Account I could select the server of my main user account for each of my aliases, which worked.
EDIT: I misstated what I did. Here is the actual solution I used:
In my Gmail account, I clicked the Gear icon > “See all settings” > Accounts. Then in the “Send mail as” section I clicked “Add another email address” and entered each of my aliases.
(To add aliases for postmaster@ and abuse@, which Google treats specially, I first had to create a Google Group for each one, with myself as the only member so I would automatically receive email sent to either of those aliases.)
In Mail > Preferences > Accounts > me@mydomain > Account Information I clicked the Email Address pulldown, selected Edit Email Addresses and added each of my aliases.
Step 2 is essentially what Dan Moren suggested except modified for my OS (12.4).