How do I back up my old iPhone before trade-in without affecting iCloud storage for my new iPhone?

I think that I would get extended storage at iCloud for a month while do the whole exchange thing. For you can get 50 GB, or for $3 you can get 200 GB, and then just go back after you're done. It's not worth $3 to worry about it!

Are you using iCloud Backup, or are you using iCloud Photos or iCloud Drive?

This is a pretty handy guide:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Deleting the old iPhone 15 Pro backup would probably free up enough iCloud space in order for your iPhone 17 to backup. There is a small risk of data loss if your iPhone 17 becomes unresponsive after that backup was deleted and before the new one was created. That could happen due to entering the Passcode incorrectly too many times on the new phone or a rare hardware failure during that time. Also, you can use the QuickStart method of transferring the data directly from your other phone instead of using an iCloud Backup for restore if it is not available.

On the other hand you have to ask yourself if 2.99 cents for an iCloud upgrade (200GB) is worth it to avoid the risk. You can easily downgrade again to the 50GB that I suspect you currently have if you don't need any additional space and as long as you do that at least a day before the monthly renewal date, you will not be charged for the additional plan.

PoutyPanda wrote: …Unfortunately, I do have the 200GB plan I’ve been paying for monthly. My photos take up a lot of space with the iCloud.

I'd do the 2 TB plan for one month, then. Really, it's just another $7, and worth every penny.