Well, after 20+ year using Mathematica I still learn something new every day. ;-)
The only thing wrong with your use of Transform field above is too many brackets, although code not in a code block sometimes gets mangled in a posting.
Below is a use of the built-in function you found, as well as an example of making your own, which is one of Mathematica's real strengths.
* and note that in my earlier post above I incorrectly used ArcTan[y,x] rather than ArcTan[x,y] *
In[1]:= (* with the built-in function *)
TransformedField[
"Polar" -> "Cartesian", (r^2) Cos[theta], {r, theta} -> {x, y}]
Out[1]= x Sqrt[x^2 + y^2]
In[2]:= (* doing it with a Rule and Replace works also *)
fromPolarRule = {r -> Sqrt[x^2 + y^2], theta -> ArcTan[x, y]};
In[3]:= (* and we can use it to define a function *)
myTransformedField[expression_] := expression /. fromPolarRule
In[4]:= myTransformedField[(r^2) Cos[theta]]
Out[4]= x Sqrt[x^2 + y^2]
