I lost all my notes in iCloud and can not find then anywhere…nor can I seem to be able to recover

Where were the Notes? See the pic below. You will get your answer

The various options that you are referring ("the second text menue") to will exist only if your Notes are on iCloud or the "On My Phone" Folder.

The 2 pics below are self-explanatory.

If you're missing notes on your iPhone, iPad, or iPod touch

Notes are always synced through Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other email Account

Any data on your device that isn't synced regularly will be stored in your iCloud Backup. With Backup turned on, iCloud takes periodic snapshots of this data to make sure it's easy to restore any time you get a new device. Between syncing and backing up, all of your data is kept safe in the cloud.

What does iCloud back up? - Apple Support (IN)

I've seen this issue occur before, and it's usually due to a temporary syncing issue with iCloud. Try the following:

• Check your Recently Deleted folder in Notes.

• Force quit the Notes app and reopen it.

• Restart your device.

• Sign out of iCloud and sign back in.

If the notes are still missing, contact Apple Support for further assistance.