I would take away the phone too - possibly for the rest of the holiday - although I know there is not long to go.
My dd went through a very testing two years aged 12/13. She really was very trying (glad to report that things are hugely better now she is 14 yrs and open to reasonable discussion and seems to have her sense of humour back!). I found it an incredibly difficult time. Most of the time when I took her phone off her, she was a child transformed! (And I have continued to have strict time limits for it now as well.)
I am sure you are not doing anything wrong at all, especially as she has adjusted well to secondary school, so try not to take it personally. As others have said, it's the combination of teenage hormones, social pressures, uncertainty and lack of confidence that cause all the angst I think. I think teens respond with "flight or fight" when they feel defensive or unsure. (Fight = all the arguing, negativity and back-chat and flight = losing themselves in their phones and music etc and ignoring eveyrone else!) Looking back, I wish I had removed myself from the negative cycle of arguing a bit more, as I can see that I got drawn in to it too much at the time which didn't help. You, being the "safe" person at home become the lightening rod for all their insecurities and worries (which are usually expressed in anger and negative ways).
The thing I found helpful was reading a book - whose title I forget - which (a) explained why teens were going through all of this and basically why they couldn't help a lot of it, owing to brain chemicals and changes etc and (b) why teens, in their fragile state, see most interactions or even mild criticisms as an attack. (If I can remember the title, I will come back and post it here.)
Presumably you have had a one-to-one calm discussion with her about the effect her behaviour is having on others?
As for the refusing to talk about puberty thing ... no worries ... just make sure she has lots of books on the subject and make clear you are willing and able to talk about it at any time (as you have already done). My dd was very clear about not wanting to talk about it all until she was ready... and then she was ifyswim.... .
Good luck op
12/13 yrs can be a really difficult time and you have my sympathy!