HDMI splitter at 120hz

but if the video feed is not going though a HDMI 2.1 port, the signal / bandwidth to the TV is limited by the HDMI port the it uses, be it a straight connection or some sort a splitter,

4K 120hz requires a HDMI 2.1 port, no HDMI 2.1 ports, no 120hz at 4K

HDMI as a digital signal it either works or it doesn’t. There is no “picture quality” and you can use any that say it support your target refresh rate and resolution

but if the video feed is not going though a HDMI 2.1 port, the signal / bandwidth to the TV is limited by the HDMI port the it uses, be it a straight connection or some sort a splitter,

4K 120hz requires a HDMI 2.1 port, no HDMI 2.1 ports, no 120hz at 4K

The LG CX has 4xHDMI 2.1 ports! The Xbox will be directly connected to it as I describe above.

eARC is not a signal splitter device. It is a feature of TVs the past few years that returns audio to an external device like a soundbar or amplifier.

The best way to resolve this would be hdmi 2.1 splitter or audio extractor connected to XSX/PS5 that splits signal to tv and to audio system, the problem is that the device like this doesn't exist, there are 4k 120hz splitters but those cant provide signal to two receivers at same time

You are actually using a HDMI switch, which is different from a splitter. You need a 1 in 2 out HDMI splitter. You will connect the HDMI from you cable/sat box to the splitter, then 1 HDMI from the splitter directly to your TV to watch like normal. Then
the other HDMI from the splitter to your Xbox one HDMI input, and another HDMI from Xbox one output to the TV. Check out the video like I posted for more info.

Watch "Xbox One Cable Box HDMI Splitter" on YouTube

https://www.youtube.com/watch?v=ryH1G3-yw-g&feature=youtube_gdata_player