docs: verify fresh npm install on Windows, macOS, Linux

[shrey16]

Goal

Verify the public npm install path on the three main operating systems.

Checks

• npm install -g bharatcode
• bharatcode --version
• bharatcode auth login
• bharatcode doctor
• bharatcode . from a small test project

Report

For each OS, note:

• Node version
• shell used
• whether browser login opened correctly
• whether bharatcode doctor passed
• any confusing copy or setup step

Safety

Do not paste OAuth tokens, credential files, API keys, private prompts, or private repo paths.