Assuming that Apple is willing to offer anything for the old phone, you could trade it in for an Apple gift card for use for future purchases.
Apple Trade In - Apple
As far as applying the value of the old phone against the cost of the iPhone 14 purchase, you need to ask Apple. But one of the FAQ items says "Your trade-in estimate is valid for 14 days after you receive your new device. It’s important that we receive your trade-in within this time frame to ensure that you get the estimated value."
Another says "If you buy an iPhone, iPad, Mac, or Apple Watch and pay in full, your credit will be applied to your original payment method up to the total purchase price after we receive your trade-in device and confirm that
the condition matches what you described. For any remaining amount, you’ll receive an Apple Gift Card by email."
That suggests that they have anticipated that people will want to keep using their old phones until the new ones are working – and that you can come up with an agreeable timing.