HDMI 2.1 to USB-C Port Cable
So I've recently purchased LG's 48" C1 and want to start using it occasionally as an external monitor for my 2019 Macbook Pro 16".
Does anyone know if there is a single HDMI 2.1 cable to USB C that will allow full 4K 120hz output to the TV, or will it require an adapter?
I've found this HDMI 2.1 cable from Belkin, and this adapter from Cable Matters, but does anyone know of a single cable that can do this, just for tidiness.
Also, is it even possible for the MBP to output more than 60hz, seeing as it itself only works at 60, I think? Not my area of expertise, I just want to get the most out of my machine and display. Thanks in advance.