Of course, while a search engine could conceivably index and search the entire Unicode codespace internet wide, such a task would likely be somewhat unrealistic and provide only limited upside.
Search engines for CJK languages do tend to work at the character level so a search for โSonaโ on a certain site run by (I think) Chinese people will turn up result for โPersonaโ.
I was involved with an A.I. startup where we had lots of meetings about what to do about all the strange Unicode characters and right now in Mastodon there is a lot of concern that screen readers will choke on ๐ฎ๐ง๐ข๐๐จ๐๐ ๐๐จ๐ฅ๐ ๐๐ก๐๐ซ๐๐๐ญ๐๐ซ๐ฌ while it doesnโt seem that difficult to squash them down to ordinary characters or treat them exactly as <b>unicode bold characters</b>