Is it possible to back up the photos on my MacBook Air to iCloud?

There is no iCloud Backup for Mac but you can sync photos with iCloud (and other devices) using iCloud Photos.

See: Set up and use iCloud Photos - Apple Support

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iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See the following Apple article for more information: Set up and use iCloud Photos - Apple Support

Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.

It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.

Also see the Apple article: How to back up your Mac - Official Apple Support

And more information on syncing in:

Set up and use iCloud Photos - Apple Support

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Access and manage your files in iCloud Drive - Apple Support

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Add your Desktop and Documents files to iCloud Drive - Apple Support

I only use iCloud Photos so can't personally recommend one. I have minimal experience with Google Photos but that is one possibility.