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-to-gif.md

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+---
+description: Turn a video clip into an animated GIF.
+---
+
+# Video to GIF
+
+Turn a video clip into an animated GIF with configurable frame rate, width, start time, and duration.
+
+## API Endpoint
+
+`POST /api/v1/tools/video/video-to-gif`
+
+Accepts multipart form data with a video file and a JSON `settings` field. This is an async endpoint - it returns `202 Accepted` immediately and progress is streamed via SSE at `GET /api/v1/jobs/{jobId}/progress`.
+
+## Parameters
+
+| Parameter | Type | Required | Default | Description |
+|-----------|------|----------|---------|-------------|
+| fps | integer | No | `12` | Output frame rate (1-30) |
+| width | integer | No | `480` | Output width in pixels (64-1280). Height scales proportionally |
+| startS | number | No | `0` | Start time in seconds (must be >= 0) |
+| durationS | number | No | `5` | Duration in seconds (0-60) |
+
+## Example Request
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/video/video-to-gif \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@clip.mp4" \
+  -F 'settings={"fps": 15, "width": 320, "startS": 2, "durationS": 8}'
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "async": true
+}
+```
+
+## Notes
+
+- Lower `fps` and `width` values produce smaller GIF files. A 480px-wide GIF at 12 fps is usually a good balance.
+- Maximum duration is 60 seconds. Longer clips produce very large files.
+- Progress updates are available via SSE at `GET /api/v1/jobs/{jobId}/progress` until the job completes.