Old Charger:New (iPhone 13) - Long-term Impact on iPhone Battery Health

I'd assume that you're mentioning the wattage, which is mainly the difference between an old and the new charging brick.

Battery degrades overtime and what you use to charge it does not make a huge impact, as long as you charge using a genuine Apple charging adapter and the cable. If you charge using a 5 watts adapter (the old one), your phone will take longer to charge and from my experience, the adapter gets really hot when charging newer iPhone.

Ultimately, it doesn't really make sense to prevent this by charging with an old adapter.

iPhone Battery and Performance - Apple Support

Using an older, slower charger from a previous iPhone will NOT degrade the battery in any way.

The rep at the Verizon store doesn't know what they are talking about and more than likely wanted to sell you accessories to benefit the store's profit.

If you have an older 5w charger, which gets really hot when using it, I wouldn't use it. It should get warm, not really hot. And again, using a 5w charger won't cause ANY issues charging the phone or have any negative impact on the health of the battery.

I'm happy to help. And its good you noticed the protection plan. I would NEVER buy one from a carrier. But I DO highly recommend an AppleCare+ Plan, which you can buy on your phone directly. Should you accidentally damage your Phone, AppleCare+ (there are two levels - AppleCare+ and AppleCare+ Theft & Loss) can really save you.

If you want the coverage from Apple, open Settings App on your iPhone > General > About and you'll see options for AppleCare+ Plans.

100% support for everything @lobsterghost1 has said, both for the charger choices and for the comments about AppleCare+ as a good option.

There is no way a lower rated charger will cause problems, except it may take a little longer to charge the battery. Slow charging (within reason) is theoretically better than fast charging which may generate higher battery temperatures.