TCL Roku TV: Apple TV app streaming image is "washed out"

We're loving Apple TV+ content, but dang, the video quality is absolutely horrible through the Apple TV app on our Roku TV.

On a recent vacation, we watched Apple TV in a hotel on a Samsung TV, and it was stunningly clear and vibrant, and the image filled the screen. Very impressive.

At home on our (admittedly aging) TCL 55S405 Roku TV, when we watch content through the Apple TV app, it has letterboxing on the top and bottom, and the image is sort of "washed out". By washed out, I mean that it seems to have an almost gray haze.

The TV's picture settings are the same for every app, and in other apps like YouTube, Prime Video, etc, the video is clear and vibrant. When I watch the same content through Plex, it is bright and crisp.

I don't want to have to buy another TV, so I'm considering just plugging in a Roku box into an open HDMI port or buying something like an ONN 4K Streamer to see if the picture quality is better.

Thoughts?