You do not own the outbuildings, but you use them
The owner insures the barn and the shop as structures. What you keep inside them is yours to insure, and what happens because of how you used them can land on your liability. Tenants on acreage routinely assume both halves belong to the landlord.
Animals you keep are your exposure
Horses or livestock kept by a tenant are not the owner’s problem, and they sit outside an ordinary renters form. If animals come with the tenancy, the liability that follows them needs placing deliberately rather than hoped into the policy.
More ground means more people on it
Deliveries, visitors, people helping with work. Controlling a larger premises means answering for more of what happens on it, and the standard liability limit on a renters policy was not sized with that in mind.