Photos app is using 123 Gb out of 125 gb on my phone, but I have 50gb of iCloud with only 97mb of photos on that. How do I make my phone photos go from phone storage to iCloud so my storage is free?

In your case you have more photos (100GB) than your iCloud storage (50GB) can hold, which is why it isn't using it. It won't store part of your library, it is an all or nothing thing.

If you want to store your photos in iCloud and free up your iPhone storage you need to upgrade your storage plan from 50GB to the 200GB plan. Then yuo can enable iCloud Photo Library which will sync all your photos up to your iCloud and you would then go to Settings -> Photos and enable "optimize phone storage".