Dear Yid,
Authorship meant something completely different to the luminaries of yore. And still, the only one (To my little knowledge.) that puts Reb Shimon as the author of the Zohar is the G”RA. If you have a good source on the Ba’al Shem and the origins of the Zohar, I would absolutely love to hear about it!
The yaavetz wrote a whole treatise on this very topic. Mitpachat Sofrim. Though I do not agree with how his conclusions are commonly quoted.