chore: update version to v0.1.13 (#2)

## Version Update

This PR updates the version index to reflect the new version detected
from the official website.

- **New Version**: v0.1.13
- **Source**: https://desktop.dl.hagicode.com/index.json
- **Checked At**: 2026-02-25T11:34:50Z

### Changes
- Updated `public/version-index.json` with the latest version data from
online API

### Next Steps
After merging this PR, the CI/CD pipeline will automatically rebuild and
deploy the documentation site with the updated version information.

---
_This PR was automatically created by the [Version
Monitor](https://github.com/HagiCode-org/docs/actions/runs/22395065831)
workflow._

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

public/version-index.json

@@ -1,5 +1,5 @@
 {
-  "updatedAt": "2026-02-16T10:11:22.0529559Z",
+  "updatedAt": "2026-02-25T09:09:14.5270870Z",
   "versions": [
     {
       "version": "v0.1.9",
@@ -509,6 +509,71 @@
         }
       ]
     },
+    {
+      "version": "v0.1.13",
+      "files": [
+        {
+          "name": "Hagicode.Desktop-0.1.13-arm64-mac.zip",
+          "path": "v0.1.13/Hagicode.Desktop-0.1.13-arm64-mac.zip",
+          "size": 170180046,
+          "lastModified": "2026-02-25T08:58:13.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop-0.1.13-arm64.dmg",
+          "path": "v0.1.13/Hagicode.Desktop-0.1.13-arm64.dmg",
+          "size": 177815521,
+          "lastModified": "2026-02-25T08:59:55.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop-0.1.13-mac.zip",
+          "path": "v0.1.13/Hagicode.Desktop-0.1.13-mac.zip",
+          "size": 175626117,
+          "lastModified": "2026-02-25T09:00:53.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop-0.1.13.AppImage",
+          "path": "v0.1.13/Hagicode.Desktop-0.1.13.AppImage",
+          "size": 184033705,
+          "lastModified": "2026-02-25T09:08:17.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop-0.1.13.dmg",
+          "path": "v0.1.13/Hagicode.Desktop-0.1.13.dmg",
+          "size": 183292691,
+          "lastModified": "2026-02-25T09:04:23.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop.0.1.13.appx",
+          "path": "v0.1.13/Hagicode.Desktop.0.1.13.appx",
+          "size": 211958096,
+          "lastModified": "2026-02-25T08:59:18.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop.0.1.13.exe",
+          "path": "v0.1.13/Hagicode.Desktop.0.1.13.exe",
+          "size": 107024968,
+          "lastModified": "2026-02-25T09:01:29.0000000"
+        },
+        {
+          "name": "Hagicode.Desktop.Setup.0.1.13.exe",
+          "path": "v0.1.13/Hagicode.Desktop.Setup.0.1.13.exe",
+          "size": 107223906,
+          "lastModified": "2026-02-25T09:09:13.0000000"
+        },
+        {
+          "name": "hagicode-desktop-0.1.13.tar.gz",
+          "path": "v0.1.13/hagicode-desktop-0.1.13.tar.gz",
+          "size": 171992012,
+          "lastModified": "2026-02-25T09:02:59.0000000"
+        },
+        {
+          "name": "hagicode-desktop_0.1.13_amd64.deb",
+          "path": "v0.1.13/hagicode-desktop_0.1.13_amd64.deb",
+          "size": 117579212,
+          "lastModified": "2026-02-25T09:03:10.0000000"
+        }
+      ]
+    },
     {
       "version": "v0.1.12",
       "files": [
@@ -837,7 +902,7 @@
   ],
   "channels": {
     "stable": {
-      "latest": "v0.1.12",
+      "latest": "v0.1.13",
       "versions": [
         "v0.1.9",
         "v0.1.8",
@@ -847,6 +912,7 @@
         "v0.1.4",
         "v0.1.3",
         "v0.1.2",
+        "v0.1.13",
         "v0.1.12",
         "v0.1.11",
         "v0.1.10",