Behavior that depends on whether you edited something else in between, or that depends on timing, is just bad. Either always backspace grapheme clusters, or else backspace characters, possibly NFC-normalized. I could also imagine having something like Shift+Backspace to backspace NFKD-normalized characters when normal Backspace deletes grapheme clusters.

As for selection and cursor movement, grapheme clusters would seem to be the correct choice. Same for Delete. An editor may also support an “exploded” view of separate characters (like WordPerfect Reveal Codes) where you manipulate individual characters.