You should be able to carry multiple power banks as long as they're below 26000 mah each (I think that's the 100wh limit converted). That said, I would check with the airline to see if they have any limit. I've carried three in the past, but rules can always change.

Also, your old power bank should work. Typically they're either USB-A or USB-C to whatever your connector is (so currently lightning, but not sure about iPhone 13s)... The cables can be swapped out. Just make sure you take the usual precautions when carrying any batteries out of devices (eg, some sites recommend wrapping the terminal heads to prevent contact.... no cables in the same package, etc.).