chore: convert NoteTypesAdapter to ViewBinding

[david-allison]

• Issue Add View Binding #11116

I did this one from scratch due to 7c11d01
With a few renames from 771bee1

How Has This Been Tested?

Screen opens and is usable on my Pixel 9 Pro

Checklist

• You have a descriptive commit message with a short title (first line, max 50 chars).
• You have commented your code, particularly in hard-to-understand areas
• You have performed a self-review of your own code
• UI changes: include screenshots of all affected screens (in particular showing any new or changed strings)
• UI Changes: You have tested your change using the Google Accessibility Scanner