If you earmarked the last burger to multiple people, it would violate serializability, not linearizability. So you should be good on that. Violating linearizability would look like this: with no burgers left, the kitchen cooks a burger, marks it as available in the DB and then shouts that it's ready. A customer hears them shout and immediately tries to order it, but fails because the customer's transaction happened at an earlier logical time than the kitchen's. Kyle is saying there are still relatively small time bounds on such violations (usually?) so it's probably not the biggest problem your restaurant has to worry about (just apologize and have the customer try again).

Dealing with money is similarly not a problem. ACH takes much longer to clear than the uncertainty window of linearizability violations. The client probably won't be able to tell the difference.