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/rotate-video.md

@@ -0,0 +1,52 @@
+---
+description: Rotate or flip a video.
+---
+
+# Rotate Video
+
+Rotate a video by 90, 180, or 270 degrees, or flip it horizontally or vertically.
+
+## API Endpoint
+
+`POST /api/v1/tools/video/rotate-video`
+
+Accepts multipart form data with a video file and a JSON `settings` field.
+
+## Parameters
+
+| Parameter | Type | Required | Default | Description |
+|-----------|------|----------|---------|-------------|
+| transform | string | Yes | - | Transformation to apply: `cw90`, `ccw90`, `180`, `hflip`, `vflip` |
+
+### Transform Values
+
+- **cw90** - Rotate 90 degrees clockwise
+- **ccw90** - Rotate 90 degrees counter-clockwise
+- **180** - Rotate 180 degrees
+- **hflip** - Flip horizontally (mirror)
+- **vflip** - Flip vertically
+
+## Example Request
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/video/rotate-video \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@clip.mp4" \
+  -F 'settings={"transform": "cw90"}'
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "downloadUrl": "/api/v1/download/a1b2c3d4-e5f6-7890-abcd-ef1234567890/clip.mp4",
+  "originalSize": 12500000,
+  "processedSize": 12400000
+}
+```
+
+## Notes
+
+- Rotations by 90 or 270 degrees swap the video's width and height.
+- Flip operations (hflip, vflip) do not change the video dimensions.