It would be useful to know what TV you're using but, all modern TV's actually display in RGB, regardless of what format the content starts as. That being the case, any content will typically be converted to RGB, from a flavour of YCbCr (YCC) colour, as encoded at the source.
For example, DVDs, Blu-ray and UHD Blu-ray are all encoded as YCC4:2:0 on the disc. This is simply to reduce the storage cost of the content as YCC4:2:0 takes up less storage than any other level of chroma or RGB. To get from that, as encoded on the disc, a process takes the video from YCC4:2:0 to YCC4:2:2, to YCC4:4:4, and it's then converted to RGB to be displayed. Either the source device or display can perform this process or parts of it.
So a couple of things to pick out from your OP. Firstly, the TV may only accept RGB 'Full' from a source device, whilst in PC mode. The important bit there being accept from the source device. There are several factors that can affect this but, it is what it is so you have to live with it.
Secondly, where you mention RGB Full, the full is an expression of the video levels used. Full = data levels or 0-255 in the 8 bit colour depth realm and 0-1024 in the 10 bit colour depth realm. 0 being black and 255/ 1024 white. If it was RGB Low, that would indicate it can only use video levels with RGB. In essence 16-235 for 8 bit and 64 to 940 for 10 bit. 16/ 64 being black and 235/ 940 being white.
Thirdly,, there's no such thing as 'rgb 4:2:2'. RGB is a colour space and '4:2:2' is a sub-sampling level of YCC, a different colour space.
Those aside, your post is still a little confusing, as you only seem to mention TV settings and not what the graphic's card is set to output. What I can pick out is that if the graphics card is set to output RGB Full, you're TV needs to be in PC Mode. Is that correct?
If it is what is the graphics card set to output, if you set the TV to Game Mode?
Ultimately, clipping is bad as you're losing colour fidelity because of what looks like a settings mismatch.
If the image looks dull, that also suggests a settings mismatch. So understanding what your graphics card is set to output and which TV you have would be a good starter.
Paul