I’ve got lots of experience with SI injections. For the more sensitive horses, 5-7 days with no weight on their back. They will be too muscle sore in the area. But we did paddock turnout starting the next day. No other work for at least 3 days. In hand work could start thereafter. After 5-7 days, light ridden work. Back to normal work at 2 weeks. These are the more chronic SI problem cases.
For my guy with the acute injury that needed several rounds of Pro Stride, the initial injections were done by a vet that had a lot of experience with racehorses and eventers. So, he worked more in a way that minimized time off. He also didn’t expand the Pro Stride with anything, so while the needles were still huge, nothing was being diffused into the muscle. With steroids, you might have sarapin or something like that and a bunch of saline. I also know one vet who will dilute the Pro Stride with a bunch of the PPP byproduct and inject the joint then put a good bit into the muscle on the way out.
Anyway, with the smaller ProStride injections, one vet will say same as any other joint, about 3 days off, then light work, then back to normal work after a week. Eventing vet said horse could tack walk or light hack right away, but I did give a couple of days off with normal turnout. I will say he was much less sore and could follow this protocol pretty easily compared to the approach of also injecting the muscle.
With the KS and everything else, OP, I think 7 days in the stall is excessive if you have access to fairly quiet turnout. But he might be too grumpy/sore for riding for at least that long. And with Depo Medrol, it’s going to take a couple of weeks for full effect anyway, so take your time getting back to ridden work. Some hand walks, turnout, and light in hand work should be fine after a couple days.