The old GoPro cameras had a standard Mini-B shell, but they weren't a standard connector. They had extra contacts for the video and audio outputs. I doubt they modified the USB-C connector to include those contacts, so I think the analog video and audio are gone from the new cameras.
You'd probably need to convert the HDMI feed to analog for OSD use. A couple options for that below. But I won't guarantee compatibility, I know there's at least one HDMI converter on the market that requires a special output mode that only works on Sony cameras.
And given the price of these adapters, it may be prudent to consider a GoPro clone or second FPV camera instead?