So he got scared because he couldn't open the door and broke the door, then he tried to fix the problem and got the dressing gown wet. then he tried to fix the second problem whilst being scared because you were angry and created a further problem with the burn.
I don't see that he's done anything that warrants punishment.
OP you got a fright and this translates in worry and anger. Above everything else what annoys you actually is the money.
All of the above is completely understandable.
I don't think he heard you over the running shower when you asked him to stop. And if he was also slightly panicked he just tried his best to get out.
He must-be quite scared over the whole episode and he really doesn't need punishment.
Talk to him calmly and acknowledge you were scared by the dangers, and you think he's probably also scared and you understand he really tried to help fix the damages, give him a hug.
As an aside, too much trust placed on him (or any child) as regards the drying rail by the fire. That should not have been there in the first place. We use a wood burning stove and the heat near it is unbelievably high.
In the great scheme of things, even if you end up paying for some of the damage, you will all remember this episode so try and stay close to each other and make him understand you were both frightened. The money really really doesn't matter in the long run. Neither one of you will remember the Christmas presents, Christmas meal etc as much as this experience. The Christmas fund really is nowhere near as important as the need for both of you to feel close right now and your DS to feel reassured. He did his very best with 10 year old judgment.
And you OP, also take 5 min for yourself to recover, a big shock for you, quite scary.
I was one of those good kids growing up but did 2 monumental mistakes as a little child that I still remember. I was not punished but I was told off big time (no shouting or raised voices just very stern telling off) but my parents also explained to me the near miss, the dangers and how worried it also made them.
One was trying to light a match on the carpet in my room. No idea why, and matches were always safely out of reach and I don't know how I found that box and why did I attempt to use it.
Another one was trying to put something in the electric socket, can't even remember what it was, a pen, a something else, no idea and don't know why.
That was pure stupidity and I was well aware of dangers of fire, electricity and all the other stuff like water etc.
And I was otherwise the most cautious child in the world!
Oh apart from swallowing a nut or something like that when my DB was fixing his bike! My poor parents, that was really scary for them.
You DS was simply trying to get out of the bathroom and it all escalated spectacularly.