feat: add interactive Test Configuration diagnostic tool in settings

[naveedious]

Summary

Adds an interactive Test Configuration diagnostic tool in the Settings UI.

Features

• API Endpoint (POST /api/settings/test-integrity): Accepts unsaved settings inputs, auto-selects a sample on-disk episode from Sonarr (or tests a custom path), applies path prefix translation, checks file access permissions in the container, and runs ffprobe & ffmpeg tail decode checks.
• Frontend Diagnostic Card: Displays real-time step-by-step diagnostic breakdown (Target File $\to$ Prefix Translation $\to$ Container Volume Permissions $\to$ Stream Probe) with error messages and duration metrics before committing changes.