docs: clarify stdio server behavior and debugging

[zuhabul]

Summary

• add a new README section explaining why running uvx mcp-server-git appears idle
• clarify stdio transport semantics (no port, no standalone daemon behavior)
• add a manual initialize command for quick liveness checks
• add MCP Inspector usage for interactive debugging

Why

• addresses recurring confusion captured in confusing documentation #521
• makes first-time setup and debugging significantly clearer for contributors

Closes #521

[Copilot]

Pull request overview

This PR updates the repository’s top-level documentation to reduce confusion when running MCP servers directly (especially stdio-based servers that appear “idle” when launched without a client), and to provide quick debugging/liveness-check workflows.

Changes:

• Adds a README section explaining why uvx mcp-server-git typically shows no output and opens no port (stdio transport behavior).
• Documents a manual initialize JSON-RPC request to sanity-check server liveness.
• Adds an MCP Inspector command for interactive debugging and clarifies when to use network transports (e.g., HTTP/SSE).

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[MukundaKatta]

+1 to the manual initialize liveness check idea. The MCP Inspector pointer
is also gold for first-time setup. One small ask: if there's room, a
copy-pastable jq filter showing just serverInfo.name + version would help
new contributors confirm the handshake at a glance without parsing the
full JSON response.