This was a massive tree and the removal of it was very expensive.
A good homeowners policy (an HO-3, for example) would cover a tree being blown down onto a house by wind, as it would be a covered peril, for both the damage to the house and the tree removal.
You said your policy was “ambiguous”: How so?
I hope you got written estimates from two people before having the tree removed, and you’ve taken steps to mitigate any further damage (as well as receipts from all of this..) Pictures are a definite bonus. While you’re gathering receipts, also gather the receipts for tree trimming done to the pecan tree over the last few years to show that you’ve maintained the property, and your claim should sail through pretty smoothly. Again, take pictures of before and after, and any damage done during or immediately after.