What should I master better for professional data science in economics and finance?
welcome to the forum. I‘m a trained economist, I do a lot of econometrics, and I work in research. My opinion (and it is only opinion of course) is that you should focus on R in the first place and consider learning Python. Both is not so hard after all.

Why? R is for free and it offers a lot of support for econometrics (it is well regarded in the community). It also is well regarded in the ML community and you can work with high spec things such as Keras, LightGBM etc. So with R you can‘t be wrong. Many top research papers in economics are done with R. Stata is good for some things (like Panel), but there are so many things you cannot do with Stata. R is more powerful.

Why Python? Python and R are „similar“ wrt what you can do in econometrics/statistics. But Python offers more flexibility in many aspects (some might disagree but this is how I see it). In essence, Python is a thing that offers you a lot of possibilities on top of working with data. So have a look at it. Can be very beneficial for your career. 

Data science is an extremely broad field. But if you focus on econometrics/statistics, many other things become relevant as well in the moment. Examples are: working with „big“ data and getting a structure into data (e.g. from online sources etc). I also think that neural nets and tree based things such as boosting will become more relevant in economics in the future. Actually outside the academic world, these methods are used quite a lot in the context of economic problems.

Final note: If you think that you cannot do both (R and Python) it would still be fine to have some knowledge/experience in both. You grow with your problems. Even if you have only little experience, you can advance fast if you know where/how to start. This can also be good wrt getting a good job.

P.S. For Python there are also some good packages/applications for economists: https://lectures.quantecon.org/py/