When I was in school around 2010 or so, a lot of the younger econ grad students were primarily interested in R. I don't think Stata's going away any time soon, but it might not be completely dominant for that much longer.
In Stata's defense: It helps that Stata is actually really good for the "running regressions" part. In particular, it gets robust standard errors right without much extra work in complex cases that would require a lot of additional code in Python or R.
R wins easily for data visualization and scripting, though. It's also much better as a skill you can "take with you". If you end up working in industry, you may not be able to expense a Stata license, but you'll almost certainly be able to use R (although maybe not RStudio).