You can “post a note” but not really “note a note”. Post is the verb, note is the subject in this case.

The verb form of “note” represents a much more brief, to jot something down in order to recall, or as to remember.

The term “post” is literally used when you publish a message or picture. Makes much more sense over “note” tbh🤷

Also, in tech speak, POST is used to send data on the wire to create/update a resource. A “note” is usually a secondary datapoint that would be sent alongside the *post* action.