chore: drop the demos

[njbrake]

Description

The demos were written at a time where writing code for a demo took time... Now in the age of CC, building demos like this is so trivial that it's not worth keeping these in the repo, the docs already cover the functionality, the dependabot noise is consistently annoying, and I see no real usage of the demos anyways.

Remove the demos/ directory (chat + model finder apps) to eliminate ongoing dependabot noise from their npm dependencies.

Add a reasoning/thinking usage example to the quickstart docs to cover the one feature gap the demos previously showcased.

PR Type

• 💅 Refactor
• 📚 Documentation

Relevant issues

Checklist

• I understand the code I am submitting.
• I have added unit tests that prove my fix/feature works
• I have run this code locally and verified it fixes the issue.
• New and existing tests pass locally
• Documentation was updated where necessary
• I have read and followed the contribution guidelines
• AI Usage:
  • No AI was used.
  • AI was used for drafting/refactoring.
  • This is fully AI-generated.

AI Usage Information

• AI Model used: Opus 4.6
• AI Developer Tool used: AoE + CC
• Any other info you'd like to share:

When answering questions by the reviewer, please respond yourself, do not copy/paste the reviewer comments into an AI system and paste back its answer. We want to discuss with you, not your AI :)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
see 108 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.