docs: organize tool pages by modality under /tools/<modality>/

Move all 157 tool pages into image/video/audio/pdf/data subfolders so URLs read /tools/<modality>/<id> (e.g. /tools/image/crop). Nest the image sub-categories under an Image group in the sidebar so the nav reads by modality. Add public/_redirects (301, clean + .html forms) mapping every old flat /tools/<id> URL to its new path so inbound links keep working. Rewrite all internal /tools links. Verified with a clean docs build (no dead links).

apps/docs/tools/video/extract-audio.md

@@ -0,0 +1,45 @@
+---
+description: Pull the audio track out of a video.
+---
+
+# Extract Audio
+
+Extract the audio track from a video file and save it as MP3, WAV, or M4A.
+
+## API Endpoint
+
+`POST /api/v1/tools/video/extract-audio`
+
+Accepts multipart form data with a video file and a JSON `settings` field.
+
+## Parameters
+
+| Parameter | Type | Required | Default | Description |
+|-----------|------|----------|---------|-------------|
+| format | string | No | `"mp3"` | Output audio format: `mp3`, `wav`, `m4a` |
+
+## Example Request
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/video/extract-audio \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@clip.mp4" \
+  -F 'settings={"format": "mp3"}'
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "downloadUrl": "/api/v1/download/a1b2c3d4-e5f6-7890-abcd-ef1234567890/clip.mp3",
+  "originalSize": 12500000,
+  "processedSize": 3200000
+}
+```
+
+## Notes
+
+- If the video has no audio track, the request returns a 400 error.
+- MP3 is lossy but widely compatible. WAV is lossless but large. M4A (AAC) offers a good balance of quality and size.
+- When the source audio is already AAC and the output format is M4A, the audio stream is copied without re-encoding.