I'm answering as someone who routinely evaluates and hires data scientists.
As a person transitioning from academic study into a private sector career, you're not going to get hired on the strength of any specific skills you have. The world of academic study in statistics, and the domain of any given company's set of problems are far too vast to hire on the basis of very precisely defined specific skillsets.
Instead, you are going to get hired because you can demonstrate a general aptitude for precise thinking, a thirst and talent for problem solving, an ability to understand and communicate abstract and complex ideas, and a diverse set of practical and theoretical skills.
So, my advice, and I'm just one guy, do what you love and develop a thirst for problem solving, nuance, and complexity. Learn a diverse set of skills, and know your fundamentals well (better than your research topic)
Oh, and learn to program.
That makes a lot of sense, thanks a lot for the thoughtful reply. Are there any particular programming languages you'd recommend
Hard question to answer without being opinionated.
My personal opinion is that it doesn't really matter, so learn the one that you like and that motivates you to keep learning. Learning your first language really well is the big hurdle. After the first learning another (and another, and another) is much, much easier because you have already dealt with the hard conceptual challenges.
But learn the language well, learn how the language works and why it was designed the way it was. Write clean code that you are unafraid to return to. Take writing code as a serious responsibility, not a unfortunate reality. This makes it both more rewarding, and a real skill you can advertise.
If you still want specific advice, I would echo @ssdecontrol, prefer a general purpose language that can do stats over a stats language that can (kinda) do general purpose.