For streaming I don't know what changes, but I can't imagine it's totally painless and hassle free. For the TV the big Q is whether the local dimming algorithm can keep up in game mode or if it gimps itself so that input lag isn't sky high. You can see in the previous image what I mean, you have 2 premium 8K TVs both in game mode but only one can keep the picture quality the same in both game mode & movie mode. Besides Sony TVs & a single Samsung model (Q90T), I haven't seen TVs be able to keep up the same PQ in both modes, talking about non-OLED.
To test it's simple: watch this video on the TV and switch between the TV's game mode & movie/cinema mode, and see if you can spot any differences particularly in relation to blooming.
https://youtu.be/VOBytpDiDuw
Thanks, I'll give that a go.
Possibly a stupid question, but watching that on my monitor in HDR - should that not look the same as when I'm running the game? Because it doesn't - it looks far better, and how I would expect the game to look with HDR switched on.