I had the same problem on my iPhone 11 Pro Max since yesterday when I updated to IOS 18 and the notes app appeared to be unresponsive and none of my notes would open. I had one large notes file which I desperately needed.
I tried all the solutions online and non worked. This included locking the note and applying a password. No good.
Some people suggested turning off syncing to iCloud but I never was using iCloud. I tried enabling and then disabling but that didn’t work. I tried logging out of iCloud then restarting the phone and logging back in to no avail.
I realised that even though the notes app appeared to be frozen some functionality was still working in that I was able to move the notes file to and from iCloud and between folders locally on the iPhone.
I realised that I could create a brand new test note file and this worked perfectly and would open and close and could be edited perfectly normally as long I kept away from my existing file. Having created a new file I disabled iCloud syncing and turned off 4G mobile data and clicked on my existing note and just left the app open apparently hung but after about twenty minutes it finally opened complete with all my data much to my relief.
I immediately copied all the text into an email that I sent to myself as a backup.
Problem Solved.
Notes now works fine as it did before the update. Just to be sure as I am an IT engineer I decided to delete my notes from both iPhone and iCloud and removed and reinstalled the notes app from the App Store to have a clean start recreating a new note from the data I copied out of the old file.
Everything now back to normal with no data loss but I really don’t like the new layout of IOS 18 and it’s caused a major headache with notes.
Hope that helps.
Good luck.