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I've a pile of HDMI cables you're welcome to try. There's a USBC to HDMI one which is pretty much guaranteed to work.
For me, I gave up on the LG monitor I had because of the cable issues. I've got a 2020 MacBook Pro which only has two USBC ports, thus, charging, display output and camera meant getting a hub which caused me no end of issues. I settled for the LG for Mac monitor which I managed to get for a decent price used. It was worth it just to have a single cable solution because of the hub in the monitor.
No, it's just an unbranded one. Oddly, I've managed to just get it to connect to a Samsung TV, no problem, so it's definitely sending signal.