Here some links in my search engine bookmarks:

Not an engine, but a search query generator: https://dorkgenius.com/

Customizable Search:
https://kagi.com/

Private search:
https://duckduckgo.com/
Https://qwant.com

Ai search:
https://www.phind.com/
https://metaphor.systems/
https://consensus.app/search/

"Old" simple web search:
https://search.marginalia.nu/
https://wiby.me/
https://searchmysite.net/
https://vhs.neocities.org/ (⚡️by google)

Forum search:
https://crowdview.ai/

Public record, libraries search:
http://judyrecords.com
Https://WorldCat.org

Reddit search:
https://conversations.aawadia.dev/find (broken 😔)

Copypasta search:
https://copypastadb.com/

Reverse image search:
https://tineye.com/

Pdf search:
http://pdfyes.com/

For more inspiration:
https://en.wikipedia.org/wiki/List_of_search_engines