By default, 4K videos shot at night with a Google Pixel 6 can be very grainy:
How can I make 4K videos shot at night with a Google Pixel 6 less grainy?
There's not much you can do. Either make the entire video darker or use some form of denoising software. Unfortunately, to get the video to be as bright as you see, it requires amplifying the image quite a bit which also amplifies the otherwise hard to see noise.