How can I repair a large hole in an interior door?

Unfortunately,you found a drill. It looks like you used a hole saw so if you have a set, use the next larger size and cut a plug from a piece of wood the same thickness and file it down to fit in the hole. Use wood filler to fill in the rest. If you have a jig saw, trace the hole on a piece of wood and cut it out and glue it into the hole. Last resort would be to get a can of wood filler, putty, and over a week, fill in the entire hole and damaged area with the putty allowing it to dry between coats.

You will never be able to repair the door so it will look undamaged. Here are a couple of suggestions to repair the door so the repair isn't obvious:

If you used a hole saw and saved the door chunk that was drilled out find how it was oriented in the door. next lay the door on a flat surface. apply tape over the opening on the inside face of the door. Remove the door latch (lock) and knob (handle).

Screw a piece of wood over the tape so it completely covers the damaged section. Screw several course threaded screws to the inside edge of the damaged section. Leave about 1" of the screw head above the wood. These will be anchor points for the next step.

At this point you have some options on fill-type. 2 part epoxy is the strongest and more costly. Car filler (Bondo) is the next best filler to use. In either case place the remnants of the drilled door piece in place (if it's large and unbroken enough).

Pour in the epoxy or press in the putty. You'll need to sand the dried putty and drill for a new latch opening.

To be honest, I would seriously consider replacing the door. Sometimes the "big" fix turns out to be the cheapest & easiest, particularly if the door is a typical indoor door and a standard size (or close enough that you can get a standard size door and trim it to fit).

However, one possibility that might work is a door reinforcer:

But (a) it will look a little out of place on a bedroom door and (b) I am a bit concerned about whether the lock will work effectively (and not just fall apart, or even worse, jam) because it is barely hanging on right now.

Not a "quality Repair", but you could put a thick "fun" sticker on one side, fill with expanding foam, sand it approximately flat and put a sticker on the other side.
If you sell the house, you will likely be asked to replace the door.