I haven't been able to get this to work since Big Sur, it stopped working in Monterey.
I use a Cable Matters USB C Multiport Adapter since I need to use DisplayPort to get full refresh rate on my 24" Dell retina monitor. I'll give some basic Type-C to HDMI adapters at try to verify the adapter isn't a problem, but I do recall this adapter working in Big Sur.
Has anyone tested this recently on Sonoma?