I noticed that the following warning has started to pop up in the log:
API warning (login): Fetching a token via action=login is deprecated. Use action=query&meta=tokens&type=login instead. API warning (login): Main-account login via action=login is deprecated and may stop working without warning. To continue login with action=login, see [[Special:BotPasswords]]. To safely continue using main-account login, see action=clientlogin.
The first should simply require updating pywikibot but the second requires us to either set up a BotPassword (quick and painless) or OAuth (less quick and painless but safer).