There, I fixed it.
Last time, I had set up POP3 for my personal account (which has too little space for IMAP anyway). Later, I tried to set up IMAP for my work account (which, for my needs, has plenty of space). That didn't work, because "authenticated SMTP" was disabled. How Microsofts own web mail client could send, presumably authenticated, mail anyway, is beyond me. Perhaps it has some special protocol, or maybe Microsoft treats its own client differently... In any case, it turned out that I, on my work account, had enough administrative privileges to enable authenticated SMTP, so now both accounts are working. Yay.
Then Google wouldn't take my money... which turned out to be my own fault. Last year, the contactless payment antenna broke in my card, despite me being careful with it. The replacement - of course - had a new expiry date. Apparently, I hadn't shared that with Google. Rather than giving me a meaningful error message, Google just said OR-PMSA-03 instead. I suppose one complicating factor was that the old card would still have been valid, if it hadn't been replaced.
FairEmail worked very well for me even in its free form. Some advanced features were unavailable and there were a discreet nag text in the UI, but it was still a very functional e-mail client, and that nag text could even be hidden for a while. Once I had verified it met my needs, I wanted to pay for it. Not sure I need reply templates or colour codes for my two accounts, but a less than $10 tool that, for my needs, is arguably better than the free options, is a bargain in my book.
So far, it has just worked for me, with almost the default settings. I turned on a "compact view" to make better use of my landscape screen, and I turned off "conversation threading", since I, and everyone I know, are too lazy to set up address books. To send messages to someone we've been in touch with before, we'll just reply to any random message from that person, making the "conversation" grouping a mess, but I do see the point of the feature among more disciplined correspondents (or people with some centrally managed address book).
I guess I'm done with this thread now. I have finally found a cheap email client that works like a charm for my needs. Would K-9, once it becomes Thunderbird for Android, gain the ability to compose rich text messages, that might become an option for me then, but unless something breaks, I feel no need to replace FailEmail.