Search in Apple Notes.app for MacOS does not work at all Today I started using Apple Notes App and populated it with little over a dozen notes. Then I tried to find a note by searching for keywords. Search does not return any result for me.
I tried to find a fix for hours today, without success.
Possible solutions
Link 1: Two suggestions
Here is a discussion that adresses the problem: Notes app search is not finding some notes
In that thread there are some suggestions

turning off notes in iCloud, restarting and turning it on again. (Did that, without success.)
re-indexing with spotlight (via command line or via System prefs). (Did that, no success.)

Link 2: Points to Spotlight issues
This discussion says it might have to do with excluding ~/Library/Containers from spotlight search. But I haven't excluded that folder.
My system

Am using MacOS Catalina, Version 10.15.5.
In Notes.app I turned off local notes. I keep all my notes in iCloud.
I can see all my notes on my iPhone and iPad. Search works there without a problem.

Edit
Search within one single note works, but
Search across notes fails
Here is a screenshot of what I see. I have only 16 notes. My search term delivers me four notes on my iPhone, but nothing on Notes.app on my Mac.

Edit 2: Decided to ditch Notes.app
After so many hours in trying to fix the broken search in my Notes.app, I decided to get rid of it altogether. Why? Because

it is opaque (proprietary database, no way to look into what's wrong)
no easy import / export (my data is siloed in this app, I can't get it out)
it is developed and supported by Apple! that means, support is minimal. Every other app developer would have solved an issue within hours (Ulysses.app, Bear.app, TaskPaper app, these kind of apps have super responsive teams, because they are small companies, but not Apple; it will answer my requests as if they are talking to retards (&quot;have you restarted/rebooted your MacBook Pro?&quot; kind of answers))

So this incident was an eye opener for me. Better get rid of the app with a handful notes, instead of using it for years, accumulating some 10k notes and then having a serious problem with the app, just when I need it.
For a search to work you have to tell the search function where to search. So if you put the notes on the icloud drive you want to click on that and then search. The search function works fine on Notes as it searches inside each note.