I can’t install google photos on my iPhone 7

You cannot.

If you have Google Photos installed on another device already, and this iPhone 7 is using the same Apple ID as that device, you may, MAY, be able to get a compatible version from out previous purchases.

click here ➜ Redownload apps and games from Apple - Apple Support

Otherwise, there is no real way to bypass the iOS version requirement.

I wanted to install Google photos on my iPhone 7 but it requires iOS 16 or later which of course I don’t have.

You are correct. If you want to install Google Photos, you will need an iPhone 8 or iPhone X.

But, as long as you are looking for a new phone, make sure that it will work with the current iOS 18 and provide 5K cellular service. That would be an iPhone 12 or higher model.