@preensie: Please can you try heading to Settings > Display > Extra brightness, and toggle this option on to see if you notice an improvement? You may also wish to toggle off 'Adaptive brightness' and manually adjust the brightness slider to improve the quality of dark scenes in the Prime Video app. Let me know if this helps.
I have the same problem. Just upgraded from Note 9 to S23 Ultra, Prime Video is now terribly dark, regardless of phone settings. Turn brightness all the way up no difference. Extra brightness it is still too dark. auto brightness on or off, no difference. I can see it light up nice when I rotate the phone so the image flips, but after half a second it goes back to dark. There is some setting conflicting between this new phone, and the Prime app.