update examples to use sdk v0.16.2

[lpmsh]

need to utilize the new createUsageEvent method on useBilling from v0.16.2

effects all examples in home-client.txt (nextjs) and index.tsx (tanstack) in the

can do away with dedicated usage events api route in favor of the catchall since it's handled in the sdk

this needs replacing:

const response = await fetch("/api/usage-events", {
  method: "POST",
  headers: {
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    usageMeterSlug: "fast_generations",
    amount,
    transactionId,
  }),
});

with something like:

const result = await billing.createUsageEvent({
  usageMeterSlug: "fast_generations",
  amount,
  transactionId,
});