[FEATURE]: Use all Appwrite services

This project doesn't show any of the advertised services from Appwrite (it shows a ping to the Appwrite API and back).

https://github.com/appwrite/starter-for-nextjs/blob/29f4675bb634b33fd1db1e3cc34b6621bd749c7c/src/lib/appwrite.js#L7-L8

Hints that the Auth and DB services are available, but they aren't used. It would be a better example if more (or all) Appwrite services were demoed.

Start with src/lib/appwrite.js at lines 7-8 and inspect the rest of the starter project to see which Appwrite services are currently only hinted at. Clarify which services should be demonstrated and how each should appear in the example; done means the agreed services are used rather than only pinging the Appwrite API.

Written by the indexing model from the issue text.