Problem with moisture in garage, what could be the cause?

[Oldboy]

If it's true that rainwater has been pushed through the panel and wind barrier, causing moisture damage to the sill, is there no other solution than to replace the panel and then install something like horizontal battens to create an air gap?

Yes, if it's true, I don't see any other solution.

Since this solution is extensive, it's of course good to try to find any other causes (and simpler solutions) and also to really try to verify my hypothesis for the cause explanation. It has been like this for many years, so another short period before taking action doesn't matter. You can certainly take the time to thoroughly investigate so you're sure you've found the right cause and the corresponding corrective action for the solution.

One investigation could be to feel with your fingers whether the paper at the exposed spots is dry or moist. Compare with dry fine spots high up on the walls. Then if the paper is fairly dry after a period of fine/dry weather and then it rains and the wind comes roughly from the right direction, go out and feel the paper afterward.
Feel free to repeat this about once a week and keep a diary, so maybe a pattern can be detected. (The diary can advantageously be an Excel sheet, making it easier to find any patterns in the moisture and the weather.)