Can't restore my backup on my new iPhone because the iOS takes up so much room there's not enough space for my backup!

The functionality of the phone didn’t change. The iOS size is bigger like it is every time a new major iOS releases. So you were going to run into the same issue if you kept your old device…or you weren’t going to be able to update the iOS because you weren’t going to have enough space without deleting some of your stuff. You don’t have to necessarily get a 16 but if you did you can see if any of the financing options would help you be able to afford (trade in options with the credit bringing the price down plus any of the no interest options such as carrier device payment plans, Apple Card monthly payments, the no interest other option through Apple, etc). Also….unless you were trying to get the largest storage a 16 Pro would not be $2000 (unless this is a different currency than US dollars)