If If I first just mention some of the strictly noise performance type of things, Con-Dom has involved plenty of things that go into performance arts category.
I suppose performance art could be briefly defined, as not everything what a band does on stage is "performance art", but lets say (as easy noise related example) Con-Dom assaulting audience with intent to provoke interaction where audience member learned something from him/herself, is already performance art. Theater or circus show not really performance art, and some of the noise may fall closer to being visual "entertainment". Traditionally "Performance art" is a term reserved to refer to a conceptual art that conveys a content-based meaning, rather than being simple performance for its own sake for entertainment purposes.
So in some cases, could be argued if Bizarre Uproar bloodbath moshpit is "performance art" unless there is for example.. hmm.. Siikala involved with some sort of intellectual content like cooking rats to signify.. something?
And don't get me wrong, this is not dismissive towards Bizarre Uproar. It can be seen as STRENGTH that work itself is purely physical and sensually vivid and vital experience, as opposed to worst "academic" conceptual art.
In case of noise, perhaps one could think merely "intentional performance" or "interaction of artist and crowd" makes it some sory of performance art... I guess we could throw in some performances of Death Squad, Vaginal Dentata Organ, Schimpfluch Gruppe, Dave Phillips, Mattin,... plenty names to drop!
In recent experiences, I feel that even bands like Jazzhand or Metsäkirkko crossed the border to performance art, as opposed to doing "show". Like BHM event, where Jazzhand did acts that may not directly involve audience, but were performing acts in certain ways I don't think needs to be dealt in detail. Metsäkirkko in same event involved audience into sound making, but also took physicality, body action, artist-audience interaction, specific time and location into process that aimed to create some sort of results that wouldn't otherwise happen.
I do not know how it is elsewhere, but in Finland there was very vivid performance art scene especially during 2000's. Lots of new blood, a lot of young female artists, festivals and such. Cross over of noise and performance arts was happening and many noise shows in Helsinki happened in space that was primarily performance art space, La Bas. In Lahti, it used to be very vivid too. I have not listed it as part of official GRUNT live show list, but I did play noise show in one of the local events. That era is long gone as far as I know and been told. Art world of current moment is probably pretty damn far from mentality that used to be there.