It's fairly trivial to add a HDMI/DP input which directly drives the panels in the headset through a mux (e.g. the Pico Neo3 Link could run standalone or from DP input), but that's probably not what you want, because in that case the HDMI source has to perform all of the 3D rendering and lens correction, using software that probably only supports Windows. If you want to be able to plug in any random HDMI source and have that rendered on a virtual screen then the headset needs a SoC with a low-latency HDMI receiver built in, so it can ingest the video and process it onboard before displaying it, and HDMI input isn't very common on these mobile SoCs.
Maybe you could convert the HDMI input into MIPI and feed that into the SoCs camera interface, but I think headsets like the Quest are already pretty much maxing out the SoCs camera capabilities just to read in all the actual cameras used for inside-out tracking. There's no bandwidth left to shove an extra HD video feed in as well.
tl;dr HDMI input that turns the device into a dumb PCVR headset: easy. HDMI input that mirrors arbitrary video: hard.