I was not asked to relate my interests to "the canon". I seriously doubt that anyone will ask you a question like that. It could be useful to be able to explain where your interests exist in relation to existing bodies of scholarship. For Brown, I think it would be wise to be able to clearly articulate how your work/interests relate directly to their faculty. They asked, "why Brown?" So make sure that you can give a compelling answer that shows why your training is best completed at Brown as opposed to any of the other great programs. I can't speak to whether they care about if your work relates to both theatre studies and some non-aesthetic mode of performance studies. I wasn't asked anything directly related to that, and it seems like an awkward interview question.
I don't remember a lot of the questions because it was some time ago. I remember the Brown question because it was so simple but I hadn't worked out an answer to it before they asked so I had to do a lot of quick thinking. It was(in jest) terrifying, though they were lovely. It was an awkward interview simply because I was trying to skype with four people at once and I couldn't really tell who was talking to me at times because I couldn't see everyone in the same frame. I was very good at articulating my own interests and hopes for a dissertation (though that has all changed since enrolling). I remember speaking with the DGS at Berkeley and I used the word "theatricality" and we had a good five minute conversation about the myriad of understandings of the term and how it related to performativity. So just be able to engage in a conversation about the keywords that you use to describe your interests. You don't have to have a definitive answer for complicated theoretical issues but you should be able to demonstrate the ability to think for and with someone else if the opportunity arises in conversation. If I had to do the whole process again, I would work on more solidly outlining what each program would allow me to do that another would not. This often has more to do with specific faculty than the institution, as I'm sure that I could be doing my project at any of the schools that accepted me but I chose my current institution for a specific reason. And remember that many of these programs, while they want to see how smart and innovative you are, also want to make sure that you mesh well with their values. Do you seem collegial? Are you confident? Are you open to critique? Those kinds of things.