Liability Coverage for a Flip

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Curious to get opinions on insurance coverage for a flip I am working on. It's a single-family house. Total gut to studs and subfloors. When I closed, I bought a Builder's Risk policy for the maximum amount I could lose. Essentially, if we have a total loss on the last day of renovation, I'm covered for the amount I could lose (basically my maximum all in amount less a conservative land value). My understanding is that this policy covers me for events such as fire, flood (except for ground up water issues), extreme weather, vandalism, theft to materials, etc. This is a complicated project, involving lots of structural issues, and I decided to hire a GC to manage it. The GC has the appropriate General and Auto Liability coverage, and the subs have the same in addition to Workers' Compensation for their employees. I also own the property in a single-asset LLC.

My first question is do I need to add liability coverage for my LLC? The Builder's Risk agent is trying to sell me on a basic, premises policy that would cover injuries to non-workers I bring onsite or slip and fall/injury claims occurring outside the property. Bringing people onsite I can control, and I do, so let's assume I am not bringing anyone onsite who would sue me. My question is more about what happens when a contractor causes injury to a bystander. For example, if someone steps barefoot on a nail outside the property, what exactly happens? I want to believe they’d go after my contractor’s liability coverage, and assuming the 2MM he has is enough, we’d be ok. So does having my own liability coverage add more protection in this sort of scenario? In other words, can the injured decide that they only want to sue me and leave the contractor out of it? I’m likely going to buy liability coverage anyways, since I think there’s always a risk for someone to get injured from slip and fall type of claims, but I’m curious whether it’s actually beneficial from a construction-injury perspective.

Second question, when the renovation is finished, and we're on the market, do I need different coverage? Is this when I need to switch to a Vacancy policy, or can I keep my Builder’s Risk/Premises Liability coverage in place?

Thanks!