Hot tubs are tricky in the realm of home insurance. Their coverage and how that coverage works changes based on how and where the hot tub is installed. Generally speaking, both you, your guests, and your hot tub are likely to be covered by your homeowners insurance.
Your liability coverage will likely cover you in the case of injuries sustained in your hot tub. Damages to your hot tub itself can be covered too, but it generally falls under accidental damage insurance, which is something you have to pay extra for. Each insurance carrier will treat, define, and classify a hot tub differently as well as what perils your insurance will cover.
You’ll want to connect with your insurance provider to make sure your hot tub is included in your coverage and find out what needs to happen to get it covered if it’s not. And if those terms aren’t especially agreeable, you might consider switching carriers.