The most specialized standard wins, so in this case I'd say HDMI.

Obviously, one cuts a small hole in the ziploc bags and runs the cable between them so that each connector can be in the correct bag.

In my system that lands in the "adapters" bin which has has a "display" bag within it.

That's still a topic of active debate

Either create a 2-dimensional categorization system or create a priority hierarchy.

It's own bag, it won't feel lonely for long :)