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/api/ai.md

@@ -240,7 +240,7 @@ Analyzes the image and applies automatic corrections for exposure, contrast, whi
 | `corrections.sharpness` | boolean | true | Apply sharpness correction |
 | `corrections.denoise` | boolean | true | Apply denoising |
 
-An additional analysis endpoint is available at `POST /api/v1/tools/image-enhancement/analyze` which returns the detected corrections without applying them.
+An additional analysis endpoint is available at `POST /api/v1/tools/image/image-enhancement/analyze` which returns the detected corrections without applying them.
 
 ## Content-Aware Resize (Seam Carving)
 
@@ -279,7 +279,7 @@ Fixes "fake transparent" PNGs where the background was removed but left behind f
 | `outputFormat` | `"png"` \| `"webp"` | `"png"` | Output image format |
 
 ```bash
-curl -X POST http://localhost:1349/api/v1/tools/transparency-fixer \
+curl -X POST http://localhost:1349/api/v1/tools/image/transparency-fixer \
   -H "Authorization: Bearer <token>" \
   -F "file=@fake-transparent.png" \
   -F 'settings={"defringe":30,"outputFormat":"png"}'

apps/docs/api/rest.md

@@ -25,7 +25,7 @@ curl -X POST http://localhost:1349/api/auth/login \
 # Returns: {"token":"<session-token>"}
 
 # Use token
-curl http://localhost:1349/api/v1/tools/resize \
+curl http://localhost:1349/api/v1/tools/image/resize \
   -H "Authorization: Bearer <session-token>"
 ```
 
@@ -42,7 +42,7 @@ curl -X POST http://localhost:1349/api/v1/api-keys \
 # Returns: {"key":"si_<96 hex chars>","id":"...","name":"my-script"}
 
 # Use the key
-curl http://localhost:1349/api/v1/tools/resize \
+curl http://localhost:1349/api/v1/tools/image/resize \
   -H "Authorization: Bearer si_<your-key>"
 ```
 
@@ -329,7 +329,7 @@ All AI tools run on your hardware (CPU or NVIDIA GPU). No internet required.
 
 Capture a webpage as an image. Unlike other tools, this endpoint accepts `application/json` instead of multipart form data (no file upload needed).
 
-**Endpoint:** `POST /api/v1/tools/html-to-image`
+**Endpoint:** `POST /api/v1/tools/image/html-to-image`
 
 **Content-Type:** `application/json`
 
@@ -346,7 +346,7 @@ Capture a webpage as an image. Unlike other tools, this endpoint accepts `applic
 **Example:**
 
 ```bash
-curl -X POST http://localhost:1349/api/v1/tools/html-to-image \
+curl -X POST http://localhost:1349/api/v1/tools/image/html-to-image \
   -H "Authorization: Bearer $TOKEN" \
   -H "Content-Type: application/json" \
   -d '{"url": "https://snapotter.com", "format": "png", "devicePreset": "desktop"}'
@@ -369,24 +369,24 @@ Some tools expose additional endpoints beyond the standard `POST /api/v1/tools/<
 
 | Method | Path | Description |
 |--------|------|-------------|
-| `POST` | `/api/v1/tools/remove-background/effects` | Apply background effects (color/gradient/blur/shadow) without re-running AI. Uses cached mask from initial removal. |
-| `POST` | `/api/v1/tools/edit-metadata/inspect` | Read existing EXIF/IPTC/XMP metadata from an image |
-| `POST` | `/api/v1/tools/strip-metadata/inspect` | Inspect metadata fields before stripping |
-| `POST` | `/api/v1/tools/passport-photo/analyze` | Phase 1: AI face detection + background removal. Returns face landmarks and cached data. |
-| `POST` | `/api/v1/tools/passport-photo/generate` | Phase 2: Crop, resize, and tile using cached analysis. No AI re-run. |
-| `POST` | `/api/v1/tools/gif-tools/info` | Get GIF metadata (frame count, dimensions, duration) |
-| `POST` | `/api/v1/tools/pdf-to-image/info` | Get PDF metadata (page count, dimensions) |
-| `POST` | `/api/v1/tools/pdf-to-image/preview` | Generate a preview of a specific PDF page |
-| `POST` | `/api/v1/tools/svg-to-raster/batch` | Batch convert multiple SVGs to raster |
-| `POST` | `/api/v1/tools/image-enhancement/analyze` | Analyze image quality and return enhancement recommendations |
-| `POST` | `/api/v1/tools/optimize-for-web/preview` | Lightweight preview for live parameter tuning. Returns optimized image with size headers. |
+| `POST` | `/api/v1/tools/image/remove-background/effects` | Apply background effects (color/gradient/blur/shadow) without re-running AI. Uses cached mask from initial removal. |
+| `POST` | `/api/v1/tools/image/edit-metadata/inspect` | Read existing EXIF/IPTC/XMP metadata from an image |
+| `POST` | `/api/v1/tools/image/strip-metadata/inspect` | Inspect metadata fields before stripping |
+| `POST` | `/api/v1/tools/image/passport-photo/analyze` | Phase 1: AI face detection + background removal. Returns face landmarks and cached data. |
+| `POST` | `/api/v1/tools/image/passport-photo/generate` | Phase 2: Crop, resize, and tile using cached analysis. No AI re-run. |
+| `POST` | `/api/v1/tools/image/gif-tools/info` | Get GIF metadata (frame count, dimensions, duration) |
+| `POST` | `/api/v1/tools/pdf/pdf-to-image/info` | Get PDF metadata (page count, dimensions) |
+| `POST` | `/api/v1/tools/pdf/pdf-to-image/preview` | Generate a preview of a specific PDF page |
+| `POST` | `/api/v1/tools/image/svg-to-raster/batch` | Batch convert multiple SVGs to raster |
+| `POST` | `/api/v1/tools/image/image-enhancement/analyze` | Analyze image quality and return enhancement recommendations |
+| `POST` | `/api/v1/tools/image/optimize-for-web/preview` | Lightweight preview for live parameter tuning. Returns optimized image with size headers. |
 
 ## Batch Processing
 
 Apply any tool to multiple files at once. Returns a ZIP archive.
 
 ```bash
-curl -X POST http://localhost:1349/api/v1/tools/compress/batch \
+curl -X POST http://localhost:1349/api/v1/tools/image/compress/batch \
   -H "Authorization: Bearer <token>" \
   -F "files=@a.jpg" \
   -F "files=@b.jpg" \