New iPhone and old iPhone and iCloud photos

My iCloud account has photos on it from many, many years ago. It stopped loading photos about two years ago when it hit the GB max.

I have an iPhone 12 max pro with photos on it from the last two years. But those photos never moved to iCloud because of the GB max being met.

I recently upgraded the GB space. There would now be plenty of room for the rest of the images. But I don’t know how to get them into iCloud without every single thing in my iCloud winding up on my phone.

an additional layer, is that my new iPhone 14 max pro just arrived today. I have not yet opened it.

Goal: to have the photos from the 13 move to iCloud without otherwise altering what is already there, and then for my iCloud content to not all download to my new phone - I want to be able to access my iCloud photos but not have them all rush back into my Photos app on my new phone.

I appreciate your help in advance, expert folks! Thank you!

Jason Fredregill