There are two kinds of DisplayPort 1.4 to HDMI 2.1 adapters. One uses a Realtek chip and the other uses a Synaptics chip. I don't know how either works with the M1 Mac.
Here's a post about HDMI adapters and HDR support.
#21
For full HDMI 2.1 support (4K120 4:4:4), the OS needs to be able to use DSC. I think Apple stopped supporting DSC in Big Sur for most cases? So you might be limited to 4K95 for 4:4:4 10bpc. But there's no way to add custom timings to macOS on M1 Macs so you'll be limited to whatever the OS decides to give you - at least 4K60
https://www.rtings.com/tv/tools/compare/lg-cx-oled-vs-lg-c1-oled/10619/21421?usage=11&threshold=0.10
4K120 is possible with HDMI 2.0 using 8bpc 4:2:0. HDMI 2.0 can't do 4K120 HDR (requires 10bpc).
A DisplayPort 1.4 to HDMI 2.1 adapter can do 4K120 without using DSC using 10bpc 4:2:2.