Hiya. I've had similar to yourself and yes it is very stressful.
In my case it was poorly sealed tiling that let water drip down and into electrics and blow the main fuse. It then dried and was okay until the next shower. It took ages to figure out what was the issue and where the water was coming from.
I didn't claim on my insurance and to be honest, if you are okay with the look of the roof, then you should be okay. Its hard to tell from the picture how bad it is, but it seems its been a couple of days so should all be dried out and should - for now - be okay.
If the water went to your electrics you would know about it. It will have evaporated now so you are okay on that front. If the plasterboard is not bowed or looking like it is likely to come down, then it should be okay to leave if you are concerned about a claim and the excess. I've had two other leaks and with the making a hole trick (its so the water doesn't build up above the plasterboard with no way "out" and bring the plasterboard down with its weight) meant that the damage was slight. I've left them like that and they were a couple of years ago.
Worst case, you would have to get someone in to replace the affected plasterboard. It sounds like a huge and scary job, but its not. The person would cut out the affected area, hammer up a new piece of plasterboard, seal the joints and plaster over it (the bit I dont think I could do). As has been said it can be messy due to all the crud on top of the plasterboard.
Good luck. I survived and so will you. Well done getting through this so far.