That is a pretty good discount for a practically just released device.
Have you checked the trade in value for your Pixel 6 Pro?
If you sell the 6 Pro you should get around $4-500 for it I am guessing then you need to pay $3-400 for the new phone. Cheaper than the 6a when not on sale.
I just got the 7 Pro and it is very nice. If battery and camera are your top priority then you really only have 2 or 3 choices. Top 2 would be the iPhone 14 Pro Max or Pixel 7 Pro and the third would be the soon to be released Samsung Galaxy s23 ultra. The Samsung will have the best camera hardware but okay image processing. It will cost the most depending on config. The iPhone 14 Pro Max would probably cost a little less have a better processor and longer support but it is esim only if that matters to you.
In terms of cost the 7 Pro is a steal compared to either other devices I mentioned. Battery life on the the iPhone might just slightly edge out the other two and the Pixel 7 Pro would probably be second.
So if Camera and battery life are the only considerations then I would probably lean iPhone but if cost, exclusive phone features, speech to text, clean Android then the 7 Pro is hard to beat.
The Pixel 7 Pro is really close in battery life to my iphone 13 pro max. The Pro max used to be a 3 day phone until iOS 16. Now it is a 2 to 2 1/2 day phone depending on use. The Pixel 7 Pro is a 2 day phone on heavy use and probably 2 1/2 on regular use. The cameras are really close to iPhone. But preference is subjective.
If I had a budget the Pixel 7 Pro for $749 is a steal right now. It costs less than the regular S22 when released and it is only a couple months old.
BTW the screen is great, the performance despite all the criticism of the Tensor G2 is great, battery life is great, basically in all areas it is a really good phone.