chore: tidy up example package.json files and scaffolding

[rishi-raj-jain]

• Add private: true and an accurate description to every example's package.json
• Remove leftover version fields and empty npm-init scaffolding
• Fix a duplicated/copy-pasted package name and make all names unique
• Standardize the .env.example connection-string placeholders
• Add missing .env.example, .gitignore, and web/ README files

[vercel]

@rishi-raj-jain is attempting to deploy a commit to the neondatabase Team on Vercel.

A member of the Team first needs to authorize it.

[andrelandgraf]

You probably need to revert the DATABASE_URL change

[rishi-raj-jain]

@andrelandgraf

• Replaced the example values (neondb_owner:...@ep-...aws.neon.tech) with generic placeholders (user:password@ep-xxx-xxx.region.neon.tech) as you shared
• Standardized every connection string to end with ?sslmode=require&channel_binding=require
• Included two .env.example files that were gitignored
• Standardized Database Connection String and OpenAI API comments to the following in all examples and CONTRIBUTING.md:

# Postgres Connection String retrieved here: https://console.neon.tech
DATABASE_URL="postgresql://user:password@ep-xxx-xxx-pooler.region.neon.tech/neondb?sslmode=require&channel_binding=require"
# OpenAI API Key retrieved here: https://platform.openai.com/api-keys
OPENAI_API_KEY="sk-..."