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/split-pdf.md

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+---
+description: Extract pages or split a PDF into parts.
+---
+
+# Split PDF
+
+Extract a range of pages into a new PDF, or split a document into chunks of N pages.
+
+## API Endpoint
+
+`POST /api/v1/tools/pdf/split-pdf`
+
+Accepts multipart form data with a PDF file and a JSON `settings` field.
+
+## Parameters
+
+| Parameter | Type | Required | Default | Description |
+|-----------|------|----------|---------|-------------|
+| mode | string | No | `"range"` | Split mode: `range` or `every` |
+| range | string | When mode is `range` | - | Page range in qpdf syntax, e.g. `"1-5,8,10-z"` |
+| everyN | integer | When mode is `every` | - | Split into chunks of N pages (1-500) |
+
+## Example Request
+
+Extract specific pages:
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/pdf/split-pdf \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@document.pdf" \
+  -F 'settings={"mode": "range", "range": "1-5,8"}'
+```
+
+Split into chunks of 10 pages:
+
+```bash
+curl -X POST http://localhost:1349/api/v1/tools/pdf/split-pdf \
+  -H "Authorization: Bearer si_your-api-key" \
+  -F "file=@document.pdf" \
+  -F 'settings={"mode": "every", "everyN": 10}'
+```
+
+## Example Response
+
+```json
+{
+  "jobId": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
+  "downloadUrl": "/api/v1/download/a1b2c3d4-e5f6-7890-abcd-ef1234567890/document.pdf",
+  "originalSize": 2450000,
+  "processedSize": 980000
+}
+```
+
+## Notes
+
+- In `range` mode, a single PDF containing the selected pages is returned.
+- In `every` mode, the result is a ZIP archive containing the individual parts.
+- Page ranges use qpdf syntax: `1-5` for pages 1 through 5, `z` for the last page, and commas to combine ranges (e.g. `1-3,7,10-z`).