To be very clear, gypsum board by itself is not a suitable or durable wall or ceiling material. It can crack in half if you lean on it the wrong way. If it's not supported at proper intervals, it will sag and crack over long time periods because it is not rigid. In fact, spanning large gaps and letting it sag is how gypsum board is purposefully bent by professionals to match smooth contours.

Gypsum board only gains strength because it acts as a system with the dimensional lumber backing that it is mechanically coupled to by screws. The tape and mud add a small amount of additional mechanical stability.

I agree with the comments about adding wood, at the very least 2x2 furring strips, to support the drywall. You're going to want drywall screws every ~ 12" in the centers of boards, and every 6-8" on edges. If you attempt to mud what you show in the pictures, it will crack and sag and possibly fall within weeks.

Once the drywall is properly supported, I recommend "no coat" flexible corner 450 or similar product as a corner edge bead for something like this. It's expensive but very durable and easy to mud.