Looks like I can lift the shed
I am assuming the shed is second hand?
Looking at your drawing I would guess that it would have originally had some kind of seal fitted into the central void in the base piece. If there is a manufacturers name on it anywhere then maybe ask them, they might be able to supply it. Or contact someone who makes similar ones.
But you do need to look at why the top plate it sits on would appear to be tilted rather than horizontal.
In your drawing the studs are shown as being narrower than the top and bottom plates, that is confusing. I would have assumed it was all 4x2, so would have expected the studs and plates to be the same width.
If it is as shown then I would guess the problem may be that because the load is off centre, and the stud is not the full width of the plate, it is causing the top plate to lift on its outer edge.
Looking at your drawing something like the below might do for the wall seal, price is per metre but any length you want.
No, it's a new shed. Just very cheap. One of these in green.
https://www.deubaxxl.co.uk/garden-shed-green-metal-10x8ft/990744/ That image is the best image you will ever see of that shed provided by manufacturers or vendors. Actual photos don't exist unless posted by people who have bought them.
I have made a wooden base with mini stud wall as described that I have just perched the metal shed on top of. There is no seal. There is nothing.
Yes, my sketch does not do a good job of shwoing teh scale of the metal base plate. The thin black line is the white trim that's covering the top stud plate. Metal base plate is not quite as wide as a 2x4 laid on its long side, from edge to edge, but the outer edge of the metal base plate is roughly flush with the outer edge of the 2x4. The trim extends further out and makes that shelf because it's cover the feather edge that is screwed to the outside of the stud plates. I might possibly have screwed the trim on its front side too high and thus forcing the top of the trim to sit high, causing the downslope towards the wall. That would be an easy fix if so. But I also think the compression from the metal wall sitting on it is affecting it in that way too.
The shelf on the other side of the shed is much narrower, indicating that the shed was not sitting perfectly central. That's not really the issue though, I never fussed about that until now, though if I lift the shed I'll see about correcting that. And that side of the shed doesn't leak as much.
Excuse me for not taking the time to do a proper drawing, but I'm tired.
You need to lift the shed and have some waterproof membrane where I've marked in red. You have to have overlap by design. Anything else will fail. IMO.
It looks like I can lift the shed. I'll need a couple of bodies to come help me, but I'll try and do what was suggested earlier - slide some DPM sheet in there and lift it up on the inside. I think I would still put Butyl tape across the metal/DPM seam though. Would help to fill that downslope as well as sealing the seam. I've considered removing the white trim while I'm at it, it could level out the shelf downslope, but I'm unsure how flush the top edge of the top cladding feather board is to the 2x4 and what would be exposed if I did, so I'm going to leave it. I'm not a tradesman, as you may have worked out.
If it isn't too late you might want to find a place that sells products for the camping RV market. They have sealing tapes and rubberized sealing products they use to seal the top of the trailers (caravans) and motor homes. Not cheap but very effective and fairly long lasting. If you ever have to do a prepare you only need to get through to clean sound material and apply the new. They will stick to themselves better than silicone does.
Pete
I bought some of B&Qs butyl tape, and while researching I have seen RV community posts, many of them talking about butyl tape, both branded and generically. So TBH I suspect what I have is just the same as branded ones.