Lost Notes on MacBook Air

As you mentioned .

When I signed back in (on my iPhone, which also signed me back in on my laptop), my notes appeared back on my MacBook Air too, except the notes that were previously on (and only on my MacBook Air). Those notes are now completely gone.

The device to be disconnected is an iPhone , if Apple ID is signed out from Mac system preferences > iCloud the Mac will be signed out from iCloud account and not an iPhone .

It’s a syncing process , say if there are many apple devices like iPhones , few Macs in an office and all are signed in with same Apple ID and password , a person signs out from Mac so all people who are synced with Mac will get signed out from their devices .

Suppose it would have happened , then any person can give command to sign out from his device , then all the devices will be disconnected and signed out from their Apple ID account , and it’s like controlling the devices .

In very short Apple ID sign out process is to sign out from an individual device .

See the articles Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

Sign in with your Apple ID - Apple Support

If you sign out of iCloud on Mac - Apple Support

Change iCloud feature settings - Apple Support

How iCloud keeps information up to date across all your devices - Apple Support

In Mac - in notes application , the notes stored in " only Mac section " won't sync with iPhone

On you Mac book if notes box was never checked , if you were saving notes in the notes application , those will not be saved in iCloud.com and will not reflect in notes application of iPhone ( even the notes box is checked in it ) .

In case if you had notes box checked in Mac , and saving notes that will reflect in iPhone , but suddenly you unchecked the box of notes in Mac , and tried to save notes that won't save , however previous notes will get reflect .

when you sign out iPhone , there is an option to check mark the notes app - When you sign out, any data stored in iCloud will be removed from your device but will remain in iCloud. Before you sign out, you’ll be asked if you want to keep a copy of any of this information on your device.

You didn't keep a copy of notes in iPhone , simultaneously the notes box was unchecked in Mac , that's the reason it didn't show in Mac .

But it doesn't mean the notes are lost ( it depends was notes box always checked in iPhone ) , if so you sign out Apple ID from iPhone again sign in with same Apple ID and password with same credentials the notes will start syncing from iCloud server