My wife purchased a standalone shed to serve as her art studio, which was installed on my primary residence. Which asset class (e.g., 3 year) would this qualify as?

Note: I'm classifying the purchase and install of this studio as an asset given it was procured specifically to be her art studio.

However, please advise if it makes more sense to consider a "Home Office" vs. a business asset.

This would be a commercial building, whether you classify it as a home office or studio.  If you are claiming it as a business use structure this would be depreciated over 39 years.