does using an older model charger reduce battery life on 13 pro

There's really nothing about a well designed USB power adapter that should result in better or worse battery life. And on top of that, the battery management system is actually in the phone, where the power adapter is just a fairly simple DC power supply. Now USB-C power adapters may be a little bit more advanced (with communications to negotiate different charge voltages/rates), but in the end they're just DC power supplies.

If you're talking about the standard 5W power adapter that Apple issued since the first iPhone, then there's really nothing wrong with using one in an iPhone although the speed of charging will be the issue. Apple always said that using any Apple power adapter with any iPhone was fine, even though some could charge at a faster rate. There are some claims that charging at a slower rate is beneficial because it results in less heat, but that's not likely to make that much of a difference. All iPhones have charging systems that charge at a maximum rate and then back off that maximum rate when it gets closer to fully charged. The rationale is that it starts producing far more heat at a higher charging rate once it gets closer to full capacity. This is something that's almost universal in modern lithium-ion charging systems.

The 5 watt “cube” that came with the older phones will work fine for charging a newer phone, but it will charge slower than the Apple 20 watt USB-C power source. If you charge overnight, as you should, the speed of charging really won’t matter. If you have an old iPad 12 watt charger that would be a good compromise; it is twice as fast as the 5 watt cube, which is fast enough for most people.

No, actually your iPhone will charge slower.

You’re good to go! 😉