Search feature doesn't distinguish between white space and non-breakable white space

I don’t see a bug here. A couple of remarks here.

Regarding single file search, there is not concept of whole word or even exact match search. There is an open FR for that. https://forum.obsidian.md/t/improve-single-file-find-search-by-adding-selection-casing-whole-word-regexp/29660

Regarding global search, "this text" is used for exact matching.