USB-C to HMDI (HDMI alt vs DP alt)

I have an Xreal beam with a DP alt output which I want to connect it to a TV through HDMI. I bought myself a USB-C to HDMI cable but it doesn't work. I tried the Xreal beam with a USB-C to DP to a DP monitor and it works fine.

Just to understand the issue and to get a correct cable/adapter, is there a USB-C to HDMI that doesn't support alt DP mode but only HDMI alt mode? If so, do I need to find a USB-C to HDMI cable that specifically mention alt DP mode compatibility?

Thank you.