I have used darktable, but doesn’t seem to fill your need as it is more a lightroom replacement than Photoshop https://www.darktable.org/

Don’t have knowledge to answer your question but you could check how home assistant does it, I think that should point you to the right direction.

If I were you, I would try to disable some/all of the image features your TV has in settings. Could be those settings that create soap opera effect.

I’m not 100% sure but I have always read that playing movie at higher frame rate than source doesn’t make video looking better. To get best results, it is adviced to have your screen frame rate matching the one from source. That being said, can’t tell you how to achieve this on linux since I only watch stuff on TV using shield TV as a player.