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/pdf/nup-pdf.md

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+---
+description: Arrange multiple PDF pages per sheet (2-up, 4-up, etc.).
+---
+
+# N-up PDF
+
+Arrange multiple pages per sheet to save paper when printing, such as 2-up or 4-up layouts.
+
+## API Endpoint
+
+`POST /api/v1/tools/pdf/nup-pdf`
+
+Accepts multipart form data with a PDF file and a JSON `settings` field.
+
+## Parameters
+
+| Parameter | Type | Required | Default | Description |
+|-----------|------|----------|---------|-------------|
+| perSheet | integer | No | `2` | Pages per sheet: `2`, `3`, `4`, `8`, `9`, `12`, or `16` |
+
+## Example Request
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/pdf/nup-pdf \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@document.pdf" \
+  -F 'settings={"perSheet": 4}'
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "downloadUrl": "/api/v1/download/a1b2c3d4-e5f6-7890-abcd-ef1234567890/document.pdf",
+  "originalSize": 2450000,
+  "processedSize": 2300000
+}
+```
+
+## Notes
+
+- Pages are arranged in reading order (left to right, top to bottom).
+- The output page size matches the original; individual pages are scaled down to fit the grid.
+- A 20-page document with `perSheet: 4` produces a 5-page output.