feat: add local PostgreSQL / env setup guide

[karlhorky]

Add a guide for local setup of the Vercel Chat SDK without the Vercel CLI, using:

1. PostgreSQL installed on the local machine
2. Manually-created .env.local file

This is a more comprehensive readme edit, inspired by:

1. various issues about not being able to register a user (the "Failed to create account" error message that many users run into)
   • ai-chatbot does not include instructions for DB migration on local deployments #731
   • Add Explicit Database Migration Step to Local Setup Instructions in docs/01-quick-start.md  #830
   • Update README.md #855
2. the comment from @sudheer-salavadi Failing to signup when running app locally #450 (comment)

[vercel]

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