depending on if we’re on a point in the timeline before they acquire hyperdrive or not (assuming the hyperdrive effectively counts as the same as a warp drive for prime directive purposes) the prime directive might not apply just because it would be a prewarp culture interacting with another prewarp culture.

It always applies. But they always have some leeway in the shows. Sometimes they’re more relaxed and sometimes they’re more strict. Depends on how far along they are compared to the federation, civilization wise.

assuming we’re talking about some interdimensional shenanigans where the two universes meet: the federation would presumably have to treat the SG universe as separate from themselves, since they have naquadah nukes and stuff which makes it slightly annoying for the federation to claim that this earth falls under federation government. Not to mention civil unrest and stuff.