Dont ever type combining symbols like letters and their accents separately. Just because it is possible in unicode does not mean it is a good idea. It causes all the problems you just discovered. In fact, the editor automatically normalizes all such cases into their combined form when first loading the text.
As for invisible characters, there are lots and lots of those. The problem with replacing them with visible characters is that you then have to keep track of when those visible characters come from the replacement and when they are part of the original document. That's not really do-able robustly.
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