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/video-loudnorm.md

@@ -0,0 +1,42 @@
+---
+description: Normalize video audio volume to broadcast standard.
+---
+
+# Normalize Audio
+
+Normalize video audio volume to the EBU R128 broadcast loudness standard.
+
+## API Endpoint
+
+`POST /api/v1/tools/video/video-loudnorm`
+
+Accepts multipart form data with a video file. This tool has no configurable settings.
+
+## Parameters
+
+This tool has no parameters. It applies EBU R128 loudness normalization to the audio track.
+
+## Example Request
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/video/video-loudnorm \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@clip.mp4"
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "downloadUrl": "/api/v1/download/a1b2c3d4-e5f6-7890-abcd-ef1234567890/clip.mp4",
+  "originalSize": 12500000,
+  "processedSize": 12500000
+}
+```
+
+## Notes
+
+- Uses FFmpeg's two-pass `loudnorm` filter targeting -14 LUFS integrated loudness, the standard for streaming platforms.
+- The source audio sample rate is preserved in the output.
+- If the video has no audio track, the request returns a 400 error.