Will 5w charger use reduce battery life of iPhone 14?

No, it won't harm your battery. It will just take longer to charge, as you are aware.

I worked for Verizon for 20 years. When I was there, sales reps were required to sell a certain dollar amount of accessories for every phone sold. I imagine it's still the same and similar for TMobile. They want you to buy more stuff (that has higher markups than the phones).

When I was at Verizon, I believe the "accessory take rate" was about $125. That means, on average, for every phone the sales rep sold, they had to sell $125 in accessories. So, you can see the incentive to imply that you should buy the more expensive item or replace something you already have.

That is false. It will not reduce the battery life in any way. It will just take a painful amount of hours to charge the iPhone and may not charge it at all if its being used.

If you already have the 20 watt charger use that. No reasons to use an old 5 watt charger at this point.

You're welcome and that is fine. You can confidently and safely use the 5 watt charger.

Ever since Apple stopped including a charger with their iPhones it has become an easy sell to uninformed buyers. That rep lied to you to get a sale.

I think that sounds very wise.

Best of luck.