> Could I make hardware with a "NotHDMI" port that "happens" to be mechanically compatible with HDMI plugs, has the exact same pinout, etc etc?

Yes there are a bunch of products that do exactly this, sometimes with the same pin out and used for video output to HDMI compatible screens (internal HDMI mods for consoles are an example), other ones that use it for completely different purposes like controller ports (the Bliss-Box adapters and MiSTeR SNAC controllers). They just can’t use the HDMI name. In fact a few of those HDMI console mods started with HDMI in their product names and changes them for exactly that reason (e.g. DCHDMI now called DCDigital for the Sega Dreamcast).