Your TV is playing a large part in the degraded visuals. It may be receiving a 720p signal from the Steam Deck, but it then needs to upscale that to whatever resolution your TV is displaying. Most TVs are hot garbage at doing this task, and will make your picture look washed out, or even pixelated.
If you aren't using the Official Dock and Charger, then you need to make sure they're delivering enough power for the Deck and any attached peripherals. USB-C is much more complex than previous generations, and not all docks/cables are created equal.
These are problems I've never encountered in my ~2 years of owning a Deck myself, but I can't give you more feedback without knowing what specific Dock and Television you're using.