Strategy can be math heavy. But there is a lot of work you can do that is qualitative too (although publishing within 4-5 years of a PhD with qualitative work is ...ambitious).
Strategy borrows from lots of fields, I particularly like this paper "THE EXPANDING DOMAIN OF STRATEGIC MANAGEMENT RESEARCH AND THE QUEST FOR INTEGRATION" for a good overview of the field. Strategy borrows from econ, sociology, psychology, etc. Edit: heres a link to the article: The expanding domain of strategic... (PDF Download Available)
All that said: learning things like diff in diff, propensity score matching, etc. may sound intimidating, but I think econometrics/data analysis is just explained poorly and can be quite intuitive (I mean, you don't have to calculate anything by hand, the computer does it for you ... you just need to identify how the data should be analyzed ...). There are some good videos on YouTube by "Doug McKee" and a book "Mostly Harmless Econometrics" that may help you.
You'll be fine, every doubts their abilities. But you were accepted so the school believes you have what it takes.