Why is the key word search function for notepad so horrible?

Performing a word search is a fundamental feature expected of any text-based app, so you're right — it's useless if it is not working.

If it is not working as that Apple Support document describes, then the Notes app on that Mac is broken in a manner that I cannot explain. Text search in general is a core macOS component, so I suppose reinstalling macOS is justified. However, what you describe is so odd I suspect it may be a waste of time. Something else is going on. Please contact Apple Support at your convenience and explain your concern. They have the ability to screen share with you (with your consent) so you can demonstrate what you are experiencing as they watch. Perhaps they have something more useful to suggest.

Ok thanks, in that case I don't have an explanation, other than perhaps I am misinterpreting what you meant by "keyword." Entering some text searches in the Notes Search field searches for all instances of that text in a single Note, or all Notes, and is not constrained to any particular text attribute. I've never experienced anything like what you are describing, unless of course I misunderstand what's wrong.

Searching in Notes is very robust: Search your notes on Mac - Apple Support

Thanks. Please let me know what they have to suggest.

Apple may suggest restarting your Mac in "Safe Mode" and / or reinstalling macOS. I would suggest that myself if not for the fact I don't think it's worthwhile, but here are the relevant links if you want to try it:

How to use safe mode on your Mac - Apple Support

How to reinstall macOS - Apple Support

If you want to try them, they are harmless enough. Then, if Apple suggests doing either one, you could say you did already and it didn't help.

What is notepad?

There are a number of different apps with that name on the Mac App Store. To contact its developer, read Contact a third-party vendor - Apple Support.