I'm having an issue with the Notes app on my Mac

Is your OS up to date?

If a simple reboot of your Mac doesn’t fix things, see if the problem still happens in safe mode.

How to use safe mode on your Mac - Apple Support 

Safe mode will often correct weird software behavior by forcing the OS to do disk repair, clear caches and other housekeeping and temporarily disables third-party mods. When you're in safe boot, the machine won’t be at its best performance, especially with graphics, but that's expected.

Does the same thing happen while in Safe mode?

Exit safe mode by restarting your Mac normally, then reevaluate the problem.

If you have another user account on the Mac and then login to that, does the Notes app work properly in that account? You can create on if necessary and it does not have to have admin privileges. If the app launches properly in another user account, then we know the problem lies with your regular account. After you've created and tested in the new account, you may delete that account if you wish.

Add a user or group on Mac - Apple Support

Delete a user or group on Mac - Apple Support

I suggest that you also run an EtreCheck (free) evaluation of your Mac and post the generated report back here in a reply. EtreCheck is a safe and highly regarded utility from a trusted developer and respected ASC contributor. The diagnostic report will not include any personal info. It simply gathers specifics about hardware performance and installed software that might be in conflict with the OS.

Please navigate to EtreCheck.com to download the utility. Be sure to enable Full Disk Access when you install the app. (System Settings... > Privacy & Security > Full Disk Access) Once you’ve run the app and created your report please post it with your reply to this message. 

Please note you must upload the full report. To see how, please click >  How to use Add Text when posting… EtreCheck Report.

We’ll use your EtreCheck report to look for the things that may be causing your problem and advise how to correct them.

So the good news is that the app is intact, but the bad news is there's some problem with the data it uses in your account. Progress. 👍🏽

I found this previous thread regarding a similar situation and the fix being related to iCloud synching. Maybe there's something helpful here.

My Notes app on my MacBook Pro keeps crashing... - Apple Community

Great! Thanks for sharing your solution.

👍🏽