Since the cause of the blown turbo appears to be owner neglect, had they done that they would have had to deny your warranty coverage, as the warranty does not cover parts that break due to owner negligence. They did you a favor.
They did. It’s in your owner’s manual. You are responsible for knowing what the manual says and following its instructions.
You can take them to small claims court if you want, but if they mount an even marginally competent defense they will point out that your turbo died because of sludge, and the sludge was caused by your negligence regarding oil changes (which, btw, they will find definitive proof of if they search your name on Google, as this thread is the top search result).
I would like to encourage you not to take the dealership to court, as they did you a big favor by replacing the turbo for you, and shops who do nice things for their customers like that should not be punished by having to deal with lawsuits resulting from them - that’s how you turn a decent, generous shop into a tight-fisted no-quarter shop.