Homeowners insurance doesn't cover any damage caused by tree roots.
Tree roots grow overtime and it's the homeowners responsibility to spot any problems with the tree roots and if needed the homeowner needs to cut the tree roots or remove the entire tree if the tree roots are causing issues with the home.
If a tree falls down on a home or garage then the homeowners insurance would cover the cost to have the tree removed and the damage to the home to repair the home would be covered by the homeowners insurance.
But just normal tree roots or tree roots that are causing damage to the home, garage, sewer line, water line etc that would not be covered under homeowners insurance and the homeowner would need to pay for that cost out of pocket.