It sounds like you have turned on iCloud Photos on your phone and can now view your photos on iCloud using Safari… correct? This is the first step.
Next, you need to confirm that iCloud photos is turned “on” on the AVP. Go to settings on the Vision Pro, then to Apple ID & iCloud (top setting), Go to section titled “Apps using iCloud” and select “Photos.” Turn on “Sync this Vision Pro.” Your photos should sync with iCloud and be available for viewing in the Photos app on the AVP. You also have the option to download the originals to the AVP (if you have enough space). This step is unnecessary to view photos on the AVP and downloading may take a while.
Adding (or deleting) photos on your phone will then be reflected on the AVP. Spatial (3D) videos taken with your iPhone 15 can then be seen in Spatial mode on the AVP. The iPhone 15 cannot take 3D photos, but any 3D photos you take on your AVP will be added to your library and can be seen in 2D on your phone.