Maybe the answer to this is easier than I think:
iPhone contains 40000 photos which are synchronized via iCloud with MB Air. In order to keep the photos on the MB Air exclusively I would switch “Photos to iCloud” on my iPhone to “Off”.
Can I do that? The idea is to delete the photos from the iPhone and keep everything on the MB Air (which then should be backed up in iCloud as before).
New photos taken with the iPhone would have to be “airdropped” to the MB Air.
I have thought about doing this, too. I hope someone “in the know” will answer!
Yes, sure.
The idea is to delete the photos from the iPhone and keep everything on the MB Air (which then should be backed up in iCloud as before).
New photos taken with the iPhone would have to be “airdropped” to the MB Air.
You can also connect the iPhone to the computer and import photos within the Photos app itself. See Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support
If you do iCloud backup from your phone, your backups would now include your camera roll. With iCloud Photos, they are not included in the backup, as they are synced with iCloud instead. So when you are between times that you AirDrop or import, you’ll still be able to recover photos up to the last backup if something happens to the device.
And if you are away from the Mac and want to look at photos, you can still use Safari on the iPhone to go to iCloud.com, sign in with your Apple ID, and view the photo roll from there.
Thanks for the “Yes, sure.”
That is my favorite answer 
When I started using iCloud to back up my iPhone I found that I could specify which app’s data I wanted to include in my backups. Just now I had to dig around to find the setting that says to back up my Photos when my phone (iOS 15.4.1) backs up to iCloud, which originally by default was set to OFF. Go to Settings>AppleID>iCloud>Manage Storage>Backups>[iPhone name] to tick on or off the various apps (including Photo Library) that you want included in your backup.
Mine’s a little different, unless I’m misunderstanding. There are many (all?) apps listed at that path, but Photos is not one of them. There is a note at the bottom of the screen “Photo Library is backed up separately as part of iCloud Photos.” That option appears for me at Settings>AppleID>iCloud>Photos, not in the “Backup” section. Which I guess makes sense, since Photos has its own iCloud sync feature, which isn’t true for most other apps. I do have iCloud+; perhaps that’s the difference? (iPhone 13 Pro Max, iOS 15.4.1.)
I think the difference between what we see is that I do not use iCloud Photos and you do. Thus, your backup won’t include the option for backing up photos but mine does.
You likely changed that before. I believe the default is to back up every app’s data.