docs: centralize SDK examples in official docs

[marandaneto]

💡 Motivation and Context

SDK README, usage, and example markdown files duplicated code snippets that can drift from the official documentation. This keeps usage examples in the official docs as the single source of truth and leaves repository markdown as lightweight navigation.

💚 How did you test it?

• Ran git diff --check.
• Verified remaining README/USAGE/example-style markdown files no longer contain fenced code snippets.
• Verified stale USAGE.md/old integration-doc links were removed or updated.

📝 Checklist

• I reviewed the submitted code.
• I added tests to verify the changes.
• I updated the docs if needed.
• No breaking change or entry added to the changelog.

If releasing new changes

• Ran pnpm changeset to generate a changeset file

[greptile-apps]

_{Reviews (1): Last reviewed commit: "docs: centralize SDK examples in officia..." | Re-trigger Greptile}