That's not how the Extenuating Circumstances policy works, nor what the "insurance" is for.
First, call Airbnb right now. Tell them what you did and why. In the future, you need to call them immediately. You may or may not be reimbursed by Airbnb for the hotel. They get to decide.
Second, if there is a natural disaster, you need to CANCEL. The Extenuating Circumstances policy is a policy to allow the cancellation without penalty. Again, Airbnb will get to decide if the Extenuating Circumstances are actually in play - you agreed to let them have the final say for this. To be reimursed, you will likely have to prove the emergency.
Third, the Host Guarantee is for damage to you, your property, or your guests while they are on your physical property. Imagine a guest slips in the shower, breaking the handle off the shower on their way down, causing water to spray uncontrollably all over the bath which results in damage to the drywall and floor and since the guest is now passed out from the blood and broken nose they suffered, it is an umbrella policy for you from the guest suing you for not having a slipguard in the bath.
You need to get Airbnb involved.