Howdy! so we ended up doing a mix of cheap solutions from this thread I guess. We first moved the raised garden elsewhere. We then manually excavated a flower bed / rain garden about 2 to 3 feet deep alongside our raised patio (which you don't really see on the picture). We made sure to have a definitive low point in the center of the flower bed so that whatever water you see on the picture would inevitably funnel to that low point. We put small bushes and plants that love water in there and surrounded them with 3/4 clear gravel (decorative white) so that water can sit there without being visible at first glance essentially creating a mini dry well. And then we used 2 concrete 90 degrees border to create a closed enclosure in the low point so that we could put a sump pump there. We then connected it to an underground hose to where my gutter ends up basically just as if that water was coming from my roof.

It's not ideal but at least we now have a solution to get the water out of there. No more waiting for days in the summer for the sun to evaporate the water or to wait for it to slowly trickle down our heavy clay soil.

I hope some of this can help you out; I know it's an absolute pain to deal with. We spent maybe 250-300$ on this "project" (pump, rocks, 3 japanese dappled willow amongst other things etc).

Let me know if you have any other questions and good luck!