You can put in an awning or covered walkway between the buildings. You can even do a fully enclosed, fully climate controlled hallway with lots of windows and doors out to the yard, etc. Just depends on how much you want to pay and your imagination.
I've seen some properties where they build ponds underneath the indoor hallway with glass flooring to see the fish and stuff in the pond. Obviously wild things like that cost a bit more then a simple awning or covered walkway.
>You can even do a fully enclosed,
And then lose all the regulatory benefit of whatever shed exemption you're trying to use, get absolutely screwed on regulatory compliance and code whatnot that you're leveraging by having it be a detached outbuilding. And then get sneered at by HN when you say the rules as they apply to your situation are stupid.