I'm pretty sure IME updates take care of it just fine... when I woke up this morning and tried out Microsoft's Japanese IME after finding out the new era name, れいわ became 令和 on the first try - no messing around with the "misconversion" data necessary.

Despite that, Gboard's Japanese version hasn't caught up yet, but I imagine that'll be updated fairly quickly, either manually or OTA.

Wouldn't the IME remember it for next time? And IME updates include it? So at most type it explicitly as two characters once per IME/device?

Yes, yes, and mostly yes.

This is no different from entering a name of someone written with a less common combination of kanji. You can either enter the word phonetically and pick the kanji you want (this trains the IME), or manually add an IME dictionary entry.

I fully expect all IME's in common use to have updates for this within days, if not already.

I did have to input the characters one by one the first time. Not afterwards. IMEs are usually good at this game.