No, that is only rstanarm not even the Python Stan’s packages do that. We have something similar that is bambi but is an interface to PyMC3 (another probabilistic programming language, PPL, in Python).
TuringGLM.jl would be the closest a quick and casual use of PPL with a nice formula interface.
If you want to use Stan in Julia checkout the StanJulia GitHub organization.
As a long contributor to Stan and a current member of the Stan Governing Body, I can attest that unfortunately Julia is not high in the priorities list of Stan. It is much focused in R and Python. But the developers and academics around Stan they obviously see what different PPLs are doing and highly praise Turing.jl as a good example of a nice PPL.