For completeness, the answer I was looking for was given in this post and this is the solution (for more details read the thread in the other post).
using SymPy
const sympy_parsing_mathematica = SymPy.PyCall.pyimport("sympy.parsing.mathematica")
s = "(Sqrt[Pi])/(2*EllipticE[m])"
ex = sympy_parsing_mathematica.mathematica(s, Dict("EllipticE[x]"=>"elliptic_e(x)"))
# option 1
SymPy.walk_expression(ex, fns=Dict("Pow"=>:^))
#:((1 / 2) * pi ^ (1 / 2) * elliptic_e(m) ^ -1)
# option 2 (should work soon after some updates of SymPy)
SymPy.convert_expr(ex, use_julia_code=true)
# :(sqrt(pi) ./ (2 * elliptic_e(m)))