I had a tree fall in our yard and onto the neighbors. Our insurance adjuster advised us not to pay for any of their damage. Strongly recommended.
Tree damage is usually not covered by insurance.
In another home, we had trees from a vacant lot fall onto our house. Our insurance paid for the damage. Any tree that fell on our house, covered. In the yard, not covered.
In the first instance, we got a letter from their attorney that we should keep our trees trimmed. We responded that they could trim any that crossed their property line.
It sounds mean. It’s why you have insurance and why they do also.