@joho But wouldn't transliteration be more what you are looking for?
'Cause Normalization just handles how the Unicode-Character is stored internally. So an 'Ä' should always 'look' the same, but the HEX-code might be different.
But transliteration converts from something into something else. And in your case you want to compare kind of based on ASCII if I see that correctly.
Feel free to check out https://andreas.heigl.org/2021/06/23/transliter-what/