I did another test yesterday around when I made my previous post and the missing terms hadn’t yet appeared until now. Trying to add the missing terms seemed to add them, but they didn’t actually appear in the list (as previously described).
Then I tried to delete the id of one of the missing terms after trying to add it again (as previously described, it does return the JSON, where I got the id from) to see if I could maybe then add it successfully again and not only did that apparently work, in addition several terms I must have added yesterday (but that were missing from the list) suddenly appeared. So deleting one of the missing terms must have flushed some sort of buffer or something that affected more than just the deleted one.