Owning a 6 Pro myself, I try to keep up on the issues my fellow Pixel owners are encountering, so I hope I can help.
By far the most common issue I've been seeing with screen replacements has been the problem of protective films being left in the various openings (both camera and proximity sensor). You can usually tell because looking carefully with a bright light, you'll see a tell-tale blue tint inside the opening. Here's an example of a Pixel 5a owner who had the same problem as you following a screen change.
Proximity sensor not working after new screen replacement - Google Pixel 5a - iFixit
Unfortunately we never got confirmation that was the issue but it would definitely be something to check.
Before you go through the trouble of opening up the phone again, you might go ahead and try the software remedies suggested by this article. Yes, it says its for a 6 Pro, but I don't see anything in the article that should be different for a 6.
How to Fix Pixel 6 Pro Proximity Sensor Issue
I did run across one other item that could be relevant; again you'll have to open up the phone to check it, but definitely something to look at in case the protective plastic theory doesn't pan out.
Pixel 6 Screen Replacement Proximity Sensor Issues : r/GooglePixel
Unfortunately, I can't seem to find any definitive information on the location of the 6's proximity sensor, but it's almost always at the top of the phone usually near the front camera. Hold the screen up to a bright light and you should see a peephole in there somewhere; that's where you need to check for protective plastic.
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