How are you planning to make backup copies of the photos library? You really need a backup of the Photos library on a separate drive. Sooner or later the Time Machine volume will fail, and then you will need at least one backup of the Photos Library, or you will have lost all photos. Having to pay for data recovery from a damaged disk will be more expensive than buying all hard disks in pairs, right from the beginning - one disk for the data, one disk for the backup copy of the data. The result of data recovery is uncertain.
As OT pointed out - Your wife could use iCloud Photos to keep all photos in iCloud and use "Optimise Mac Storage" to save some storage on the MacBook Air, but she would still need a backup copy of her photos library or at least the photos in the library to be able to recover accidentally deleted photos. iCloud Photos does not offer an archival history to recover older photos that we already have deleted. (iCloud Photos Library: Keep regular backups of your iCloud Photos Library - Apple Community). The original photos photos can be backed up by exporting them to the Time Machine disk, but backing up an optimised Photos Library is a lot of work: How to back up an optimized iCloud Photos Library - Apple Community
