HDMI Adapter Not Displaying to TV

So, I’ve got an interesting issue. I was hoping to display something from my iPad Pro (2021, M1 model) on the TV, and hooked it up via HDMI with the HyperDrive 4-in-1 adapter that I’ve got. However, nothing would display on the TV. The iPad kind of seemed to recognize that something was plugged in (Volume setting in Control Center changed to “Dock Connector”), but the external monitor would not show up in the Display and Brightness settings page. I’ve tried the usual restarting and unplugging/plugging things in tricks, and the other parts of the adapter work (USB A port, headphone jack, etc.).

I also tried using the adapter with my partner’s iPad Air (2020), and for some reason it works on their device perfectly, just not mine. Is there something odd about the M1 iPad Pro that makes it not work work with this type of adapter?

Any help would be appreciated.