Photos app backward compatibility

Your best bet is to use iCloud Photos-- it's the only way for different versions to use the same Library. If a Mac has iCloud turned on in Photos, then its local Library will upload all of its pictures to iCloud, and it will download any that it doesn't have, keeping all the connected Libraries in sync. And you can see the pictures on you iPhone, as well.

It's also true that if you delete a picture on one Mac, then it will be deleted on the other, maintaining the synchronization. So be sure you keep a backup on your hard drive--for instance, keep a copy of the local Library in another folder, and refresh that copy from time to time.

The only real downside is that iCloud costs $3 a month for 200GB of storage. For me, it's been worth it.

I second that advice. iCloud Photos is one the best tools in the Apple universe, allowing us to use the same Photos Library on multiple platforms, independent of the system version. I can work with my Photos Library on my iPad, my iPhone, my Apple TV, my older Mac with macOS 10.14 Mojave as well as on my most recent MacBook Air with Sonoma. The only thing that will not work on a Mac with an older system version is the Shared iCloud Photos Library. It requires at least macOS 13 Ventura. Photos you move to the Shared iCloud Photos Library will not be visible on a Mac with with macOS12 or older.

As an added bonus iCloud Photos is giving us an offsite storage, so we can recover the photos from iCloud, if our devices are getting damaged or lost or stolen.

It's not possible.

Feature requests go here:

Feedback - Photos - Apple