I would consider the av rack 15' away. Might be a headache come a 20' run for 4K, but for a short walk, and some sort of easy way to control gear, it would be on the radar
and likely a far better solution since both sides are open. (Sometimes ideas are just stepping stones, and just part of a progression to a better solution.)
No reason those home theater seats couldn't be a sectional, or a loveseat + single seat seating solution.
You could simply do a hinged panel to hide the deep side window. The idea being to have a dark room, for best video performance, and yet still have easy access to the
window, to air the room. You don't have more then 2' of room depth to give up, but those panels to hide the windows, needn't eat up room depth. They just need a purpose in
the room's final décor, to effectively disguise them.
You might not need to replace those doors at all. They could stay in place with one locked down. Or they could get mirrored panels put in, and then be blanked off inside.
Much of how I would do such a space, is about the interior look of the room you would be after, and about if one can do some DIY, or the overall budget to work with.
You could still panel off one door and create a bit of a feature wall entry look. I've often thought of a hdtv movie poster light box and a small bit of feature wall as a way to eliminate
one door of a French door. Basically remove the door and build in a new section of wall, with a proper frame for the remaining door.