Notes on Apple Watch

The Notes App is not an available option for Apple Watch. Whether it's obvious or not, Apple hasn't made this available.

Since this is a user to user only forum, we cannot do anything to help with this. And Apple doesn't actively participate here.

You can let Apple know you'd like to see this option in a future release by providing feedback here --> Feedback - Watch - Apple

Use Reminders: First delete the native lists (Schedule etc) Then set up your own lists (eg, notes, shopping, info,etc). Paste a note from somewhere else or just use Reminders for all your lists. Reminders has a watch complication which allows scribble or voice input. Syncs immediately with iPhone & iPad if you set it up in iCloud. (May need to power off both devices and then power on again)

Drafts can be used, which is a notes sort-of app on the Mac, iPhone and Apple Watch

https://apps.apple.com/us/app/drafts/id1236254471?platform=appleWatch