You need vertical backing or split the next adjacent stud and seams over studs are the correct process.

It will actually be easier to fix if you make the hole bigger. Any drywall needs backing at all seams for large pieces.

Cut out the drywall to the left(in the picture) to the center of the next stud.

Cut the repair piece to overlap the flange on the surround. I would use a factory edge as the overlap edge.

But no, you don't need an L-shaped piece to properly fix it. 2 rectangular strips are fine as long as they end on studs, as advised above.

This can be fixed without any drywall work by using PVC trim. First, cut out a bit more drywall at the side so you can slip a 2x4 stud behind the unsupported drywall. Butter the front and back edges of the stud with construction adhesive, put it in place and screw the drywall to it. Rip long shims from pressure treated lumber to build the shower flange up to the level of the drywall and nail them in place. Now you can trim the shower/tub side and top edges with 1x4 or 1x6 PVC trim, caulk it, paint it and - boom - you're done.

Use these. I use them all the time. Great little invention.

Finish the seam with tape and hot mud, it dries stronger than the premixed stuff.

No need to remove any additional walboard. When you're cutting the narrow strips of drywall, take care to not break the core.

A little bead of liquid nails polyurethane construction adhesive around the flange of that shower stall will help hold the drywall to it. Don't use so much that it squirts out.

I would do this in about 2 hours total; drywall, taped, textured, and touch up paint.

Or you could buy a plastic trim kit and install that. Probably take the same time.

Here is a link that might be useful: instaback drywall repair

I don't understand how the insta-back things are any easier than cutting to the next stud? Its neat, just don't think its that much of a time saver.

I don't understand how the insta-back things are any easier than cutting to the next stud? Its neat, just don't think its that much of a time saver.

Without knowing how close the next adjacent stud is, I would not use that system, because any drywall cannot have a greater than 3" free float, IE. unsupported, and with Aidan's recommendation, you'd have a potential 10" free float.
Also, when a shower door is installed, there would be the potential for vibration cracking.

If you had doubled up that stud on the left, the issue would be non-existent. Now the shower is in place, I don't know how you'd attach another stud without taking out more drywall. But in reality, drywall is easy to remove. go ahead and open up the wall on the left to the next stud

You can put as many instaback plates as you need for support along the top. 2 between each stud is enough. 3 if you want to go crazy.

The patched piece is just as strong as a continuous sheet, as long as you mud and tape it correctly.

The correct way is to use hot mud. Force plenty into the seam, place the tape, skim over it to set the tape in the mud.

An hour later when the mud is dry, skim over it with another coat of hot mud.

I've used these things for over 10 years and never had a problem. It's really the best drywall patch system for small pieces.

Anyone who knows drywall, who tries these things, will be sold. Professional time costs money, and these save a bunch of time.

Just wanted to thank everyone for all of the advice. Going to try to get this done tomorrow. Will let you know how it goes.

Thanks