If a timing belt brakes during operation, it could damage the engine. However, the damage will depend on the design of that specific engine.
It is important to get the belt inspected at factory recommended interval and replace when it is due.
Keep in mind that sometimes a timing belt can brake due to other component like a seized tensioner for the timing belt.
As for the broken belt in your vehicle and the warranty for it, you will have to contact the dealer that installed this for you. As the warranty can vary on a dealer installed component.
I attached diagrams for your reference.
Please let me know of any questions.
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Saturday, September 25th, 2021 AT 9:14 PM