Shower leaks can be a lot of fun to find and repair...
However, being a bathtub that only leaks when showering rules out the drain...
So all you have left to check and this list is by no means complete is:
The shower arm connection at the drop ear 90 in the wall.
The shower mixer valve.
The diverter tub spout.
Leaking escutcheons & face plates.
Additional grout and caulking problems.
Tub overflow plate gasket.
Things in the wall like windows, soap dishes, shelves, wash cloth racks, etc.
Sloppy placement of the shower curtain.
Tub installed off level.
And some other stuff I'm not thinking of at the moment...
Your leak could be one of the above or, any combination of them...
A good place to start is taking the faceplate off the mixer valve and looking in at the valve and inside the wall with the shower running to see if you see anything.
Also check the bottom of the tub spout where it meets the wall where there is a drin hole to see if it is blocked or, water is coming out there.
A plumber may have a small inspection camera such as the Ridgid Micro-Explorer which can go through a small hole drilled in an adjoining wall to have a look inside the wall to see where the leaks may be.