If possible, I would also see if you can bring your trade-in phone to an actual Verizon store and have them take care of sending the phone. I just recently dealt with an annoying headache on T-Mobile where I traded in my daughter's iPhone 8 for an iPhone 12, but since they didn't have the 12 in stock at the time, we waited for it to be shipped to us at home. Then I reset the iPhone 8, packed it up securely, and sent it via UPS using the mailing label they gave me. Everything seemed fine until I suddenly noticed I wasn't getting the bill credits for the new phone, and found out that the T-Mobile receiving facility was claiming that the phone screen didn't work, and therefore the trade-in promotion was void. Fortunately, after some wrangling on the phone, the T-Mobile rep said that the receiving facility could not produce photo evidence of the phone not working, and so they agreed to give me the original bill credits from the promo.
The important thing they told me is that if the trade-in phone had been sent by the T-Mobile store themselves (i.e., if they had the iPhone 12 in stock at the time and I could've finished the transaction when I brought the phone in the first time, proving to the store rep that the phone was working), then it wouldn't have been my responsibility at all if the receiving facility claimed the phone wasn't working (since it was working when I showed it to the store rep).
If you don't have any other choice than to mail your trade-in device, then I recommend taking multiple photos or a video of the phone's display working right before you pack it, and also show how secure your packing is. Then you could show that proof if they claimed that the phone was mishandled by you at some point.