Yes, you mentioned normalization and I didn't correct that, because indeed, grep can't do that. But you also just said "Unicode search," which is a pretty general term. GNU grep is certainly Unicode aware, as I demonstrated. It just doesn't solve every use case you want. But it does have Unicode-aware character classes and also Unicode aware case folding.

A grep tool that did normalization would be extremely slow. You'd probably be better served by a specialized tool. Or even better, it should be possible to write a fairly simple wrapper that puts everything into your desired normal form before searching.