Horrendous service and cheating by Apple store and customer care

I had an absolutely fine working iPhone 10. The only issue was Face ID had stopped working a couple months back and battery life was at 78%. Although I live in New York, on my recent visit to California, I was passing through Los Gatos, I thought of getting my battery replaced. The Genius Bar attendant was told about Face ID not working and they told me I would be charged $69 for battery replacement. When I went back an hour later, they said while opening the screen, apple damaged the screen, because of which the phone is now dead. Even if they replace the battery, the phone is essentially dead and will not work at all. I was flabbergasted. The options presented to me were

1. Take the damaged dead phone as is

2. Buy a new phone.

3. Swap the damaged phone , like for like, for $600.

I argues and argues with the tech folk and also the Los Gatos store manager for about an hour, asking them when I bought an absolutely fine working phone to their store for a simple battery replacement, why should I be fined and penalized for no mistake of mine. Clearly they had damaged the phone. They kept saying that my phone had a 3rd party screen, which is not true because I never got my screen replaced. But of course, they wouldn't listen to me.

Since I was traveling in an unknown place, and they broke my absolutely fine working phone, I had no choice but to buy a replacement unit. The manager gave a 10% discount as a huge favor to me. When asked who can I reach for complaint, because I am having to Pay almost $550 dollars instead of $69 for no fault of mine but Apple store being completely at fault, they asked me if I want I can call Customer Care.

Now that I got a replacement unit, I called up customer care. Its been a week since and I still have no resolution. The customer care says that the final authority lies with the store and they will have to partner with the store. And the store is just not budging. Forget getting a refund, they haven't even offered a gift card for a future credit of any sorts. This kind of behavior is something you would not expect from either the store or Apple Customer care at any level. That too with a customer who has been with them for 15 years. And either of them refuse to give me information on any further escalation.

How do I get this resolved? I am at a complete loss here. Hopefully someone will be able to guide and help me with this here.