Hi C,
Welcome to Permies.
I am not a professional builder, but I have done my fair share of remodels and helping others. A tongue that is only 1/2 inch deep doesn't sound like
enough. I love timber framing with joinery, but I think there is a reason they tend to use bigger pieces. You could probably do it with all 4x4 lumber, but I worry that mixing the 2x lumber will complicate things more than needed. Is there a reason you want to use joinery versus a "stick" built shed?
Sometimes I can get enamored with a particular tool or technique and try to force it into my situation. I think sometimes we need to step back and say... what is the best option here, regardless of what I like. And maybe it still is joinery because you want to try it out. That is awesome. I would just get some bigger pieces of
wood and look up some videos on the various types of connections. If a stick built frame would work better here, why not give that a try?
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"When the whole world is running towards a cliff, he who is running in the opposite direction appears to have lost his mind." C.S. Lewis