Dealership burned the paint buffing my ceramic coat - is this fixable or am I stuck with it?

That haziness is almost certainly a rotary burn, or at least evidence of over-aggressively pressured contact. When a buffer sits in one place too long, the friction and heat generate a burn mark, which is essentially a dull patch where the clear coat's integrity has been compromised by excessive heat and friction. You are definatly not screwed. This is a common, fixable mistake when a tech pushes a machine too hard without proper pressure monitoring.

The short answer regarding repair is that a quality proffesional detailer can absolutely buff this out. It is a polished stain, not necessarily a catastrophic structural damage, but it does require a professional touch, likely more than just a simple polish. You need someone who understands paint correction to address the heat damage properly, which usally means using a more aggressive compounding stage first, followed by a finishing polish. My advice on how to approach this is to go back to the dealership, but not in the service bay initially. Ask to speak to the sales manager or the general manager of the service department. Explain that during the ceramic application you noticed a burn mark caused by their technician's use of a rotary polisher. Since the coating package came with a lifetime warranty and the car is brand new, you are entitled to them making it right under the terms of the service they provided. You need them to fix the cosmetic damage their employee created. If the dealership tries to push back, insist that since the car was allready in their care and they are responsible for the pre-sale condition of the vehicle, they must perform the paint correction work themselves. You can bring the car in and state that you want them to use their factory methods to buff out the spot. If they refuse, then and only then should you take it to an independent detailer, but only to get a written estimate and a report on what they did, so you have documentation of the neccessary correction before committing to the cost.

Take pics of that spot in direct sunlight with a timestamp before you talk to anyone. I had a similar spot show up on my truck after a dealer-installed package and when I went back a week later they claimed it was 'rock damage' since I'd been driving it. Photos saved me. Also worth checking the panel with a paint thickness gauge if you know someone with one, just so you know how much clear coat you're working with before anyone starts compounding on it.

This same thing happened to my brother's SUV a while back, dull oval spot on the door from the shop that put some protective stuff on it. He made the dealer pay an outside guy to fix it and it came out looking normal again, so don't panic. One thing I never thought about til then, once they polish that spot smooth again, doesn't the shiny coating they put on come off with it? Does the whole hood need redoing or just that patch?

Had this exact thing happen on my wife's SUV a couple years back, dull ring on the front fender from the paint protection film install. What worked for us was making them let me watch the correction in their detail bay, then checking the panel outside in the sun before I drove off. They fixed the burn but 'forgot' to redo the coating on that panel until I pointed it out, so keep that in mind since they polished through whatever they applied. Also don't let them hand you the car at dusk or on a cloudy day, that's the oldest trick in the book for hiding swirls.

Whatever you do, don't let the dealer's own detail guy have another crack at it first. That's what happened with my old sedan, their tech tried to polish the spot out himself, made it cloudier, and then acted like it looked that way from the factory. The independent guy I found later took his time with a dual action machine and a fine finishing polish and the mark basially vanished. He told me factory clear is thinner than most people assume, so you want someone patient working on it, not someone aggressive. Get it written up before anyone touches the hood.