As above, make a polite, insistent fuss. Research people in the chain of command. Make sure the garage know you’re not going to go away, make them WANT to help you to get you off their back and onto Head Office’s.
I had a Honda Accord diesel which died just out of the 3 yr, 90000 mile warranty. After a little prevaricating, they paid. Took a while, but they sorted it out after an initial quote of a similar value to your friend’s. In the end, they wanted to investigate, as they were starting to see a few problem engines, and I think this tipped it. Was about the chain that ran the oil pump in the end.
I would hope that Volvo would take a similar view of their reliability reputation as Honda did for me. Volvos have a reputation of lasting for hundreds of thousands of miles, 30k is NOTHING.
Revert to social media if you get nowhere, but don’t get angry on their quickly, just that polite insistence. If you’re struggling to find out who to contact, ask that question on Social Media perhaps, wanting a specific name or asking that a senior manager contacts you.
Good luck.