Implement VPN proxy/profile support

[francomano]

Description

Add first-class VPN/profile support so ProxyDoctor can diagnose routes that are not represented by a simple HTTP/SOCKS proxy URL.

Scope

• Add a clear VPN/profile mode in the CLI and server API.
• Detect active tunnel interface and route used for the target.
• Compare direct route vs VPN route where possible.
• Report public IP, DNS resolver behavior, TLS and port connectivity through the selected route.

Acceptance Criteria

• CLI exposes a documented VPN/profile mode.
• Server API accepts the same mode.
• Diagnosis report includes interface/route evidence.
• Tests cover missing VPN, active VPN and invalid profile cases.

[francomano]

Codebase starting point: see docs/ISSUE_STARTING_POINTS.md for the concrete files to start from for this issue.