Because the problem occurs specifically in the Find field within an individual note, rather than the main Notes search, focus on Command-F.
Apple documents this function by having you open the note, click in the note body, press Command-F, and enter the search text. (Apple Support)
You have already quit and reopened Notes, restarted the Mac multiple times, and reproduced the same behaviour in Safe Mode, so those steps do not need to be repeated.
Open an existing note, click in its body, press Command-F, and type a word that appears in the note.
Check whether the matching text is still found and highlighted even though the typed characters and cursor remain invisible.
Then create a new note and perform the same test. Also type normally in the note body to confirm that ordinary text remains visible.
Try Command-F in another application, such as Safari or TextEdit. This provides a comparison with another Find field.
The next useful test is a temporary macOS user account.
Open a note there and perform the same Command-F test. If the behaviour differs between the two accounts, that result can help narrow down the problem.
For now, avoid deleting Notes preferences, signing out of iCloud, or removing Notes data.
Finally, check System Settings >> General >> Software Update for an available update.
Apple states that macOS updates also include the built-in Notes app. (Apple Support)
If no update is available and the problem remains, include these test results when reporting the issue to Apple.
Apple Support — Search your notes on Mac
Apple Support — Update macOS on Mac
Use the Product Feedback - and make it known to Apple regarding this ongoing issue