Short answer: Apple Notes is well protected against outsiders. Notes travel to iCloud over an encrypted connection and sit on Apple’s servers encrypted with AES-256. What it is not, by default, is private from Apple: for an ordinary note, Apple holds the key. Two settings change that. Locking a note makes that note end-to-end encrypted, and Advanced Data Protection makes your whole Notes library end-to-end encrypted.
The rest of this page is the detail behind that answer, taken from Apple’s own security documentation, and a plain view of what Apple Notes cannot do that a dedicated encrypted notes app such as Dash can.