docs: streamline and enhance README (setup, API reference, troubleshooting)

[naaa760]

Description

#15

• This PR overhauls the project documentation to make it clearer for new and existing users.
  Key highlights:
• Streamlined README
• Added quick-start and installation instructions for uvx, uv, and pip.
• Clarified API-key setup and Claude Desktop configuration.
• Re-wrote the tool reference with parameter tables and runnable examples.
• Added a short “Usage Examples” section covering common workflows.
• Introduced troubleshooting tips for the most frequent errors.
• Added badges and improved formatting for better readability.

Consistency & clean-up

• Fixed code-block fences, table alignment, and markdown linting issues.
• Ensured no functional code changes; this is a docs-only update.

Motivation:

• New users reported difficulty understanding setup requirements and practical usage.

These changes provide:

• Faster onboarding with copy-paste commands.
• Explicit guidance on the most common tasks (searching, creating issues/tickets, sprint planning).
• A single, authoritative source of truth (one README).