Unless the new emperor messes things up and chooses a single-character name that's already in Unicode. (That'll teach these computer whippersnappers who's boss!...)
I don't envy all the people having to update Japanese calendar or text-processing software. And things will be even more hectic if the current or new emperor dies unexpectedly. Luckily for tzdb, though, Japan does not change its *clocks* when it gets a new emperor, so we will be off the hook on this one.
It have already been announced that the new era name will have 2 characters. Japan specifically asked for a code point in Unicode BMP for legacy systems. That should make thing easier to most people but also not quite sustainable due to the limited space in BMP If era name changes are abrupt due to change of emperor or other reasons, realistically people would just use old era name until updates are ready. For tzdb, iirc the era name info is also stored in some notes comment. That could be updated too.