docs: fix directory mismatch in installation steps and resolve brokenschema link

[Mohit-001-hash]

Description

Executed a comprehensive cleanup of the README.md to fix multiple formatting and rendering issues:

1. Restored Tech Stack Badges: The ## Tech Stack section was completely blank. Restored all the Shield.io badges representing the project's architecture.
2. Fixed Roadmap LaTeX Bug: Restored the broken LaTeX mathematical expressions ($$x$$) back into standard interactive GitHub task lists (- [x]).
3. Fixed Code Block Formatting: Removed empty trailing lines inside the code blocks across the "Setup" and "Environment Variables" sections, and added proper language tags (bash, env) to restore syntax highlighting.
4. Tightened Table of Contents: Removed loose vertical spacing from the Table of Contents for a cleaner layout.

Type of Change

• Bug fix (Documentation rendering bugs)
• New feature
• Breaking change
• Documentation update

Testing

How did you test this?

• Local development (Verified in Markdown previewer)
• Manual testing (Checked link routing and task list interactivity)
• Automated tests added

Checklist

• Code follows project style guidelines
• Self-reviewed the code
• Commented complex code
• Updated documentation
• No new warnings/errors
• Added tests (if applicable)

Screenshots (if UI changes)

N/A - Markdown documentation updates only.

Related Issue

Closes #82