Lightning Digital AV Adapter [Lightning to HDMI] cannot output game audio but USB-C to HDMI can?

So I'm trying to connect my iphone to my monitor via HDMI using Apple's Lightning Digital AV Adapter but I'm not getting audio in games.

When I try the same thing with my iPad Pro using the Belkin USB-C to HDMI that Apple sells & it works.

As in both cases if I connect it will show screen & I can hear sound if say I open Apple music or youtube. I'm wondering if the issue is that Lightning is simply incapable of the bandwidth/data speed in transfers anywhere near USB-C. *The audio is output via 3.5mm to speakers.*

I don't know what the Lightning Digital AV Adapter's capabilities are because apple for whatever reason doesn't list that info & I don't have the packaging so not sure if was listed in there. But beyond the inherently superior bandwidth & transfer speeds for the USB-C to HDMI adapter the latter supports HDR with resolutions up to 4k @ 60Hz & HDCP 2.2 per Belkin's tech support.

I'm wondering if it is indeed just the limitation of the Lightning standard & I'm simply out of luck using my iphone to monitor for gaming purposes until Apple either joins the rest of the world in USB-C for their iPhones are bulls some greenwashing let's get rid of another port. Apologies for snark just supremely annoyed having purchased adapter & tossed packaging only to realize likely won't work.

Any insights appreciated. Tried with everything from COD mobile to tetris but no audio in game. I presume this wouldn't be an issue with the games themselves given I tried multiple developers/workloads.