Is that broken connector on the door, or the mirror side? If the mirror side, you may have aftermarket options.
On one of the forums (here or Bronco6G) somebody was posting pretty exotic mirror upgrades: the forward edge of the mirror had a sort of ditch light array, giving you a wider (to the side) illumination. They were kind of pricey, so I didn't read through the thread, and don't know if they work off the headlight circuit or an auxiliary switch. Also, I don't know if they would integrate the blind-spot alert system.
My point is, there is at least this after-market mirror that has an interesting feature--but at a pretty penny. So if you're facing a $1,000 repair, you might consider a $2,000 (or so) upgrade.
Perhaps somebody remembers the name of that after-market mirror and can provide a link?
Last thought: a few people have posted images of their (tragically) crashed Broncos. 😔 Message them and see if you can obtain their mirror as salvage.
Good luck--we're all pulling for you!
Edit: Found it! Maybe this is your solution:
https://www.oraclelights.com/produc...-bronco-led-off-road-side-mirror-ditch-lights
And a lot cheaper than I had (mis)remembered! And who knows--maybe you can sell your other mirror and come out even.