docs: 添加在线文档的 workflow 构建流，修复一些问题

.github/workflows/doc.yaml

@@ -0,0 +1,39 @@
+name: Build Docs
+
+on:
+  push:
+    paths:
+      - 'docs/**'
+
+jobs:
+  doc:
+    if: ${{ github.ref == 'refs/heads/main' }}
+    name: Build documentation
+    runs-on: ubuntu-latest
+    defaults:
+      run:
+        working-directory: docs
+    steps:
+      - name: Checkout repo
+        uses: actions/checkout@v4
+      - name: Setup bun
+        uses: oven-sh/setup-bun@v2
+        with:
+          bun-version: latest
+      - name: Install dependencies
+        run: bun install --frozen-lockfile
+      - name: Cache dependencies
+        uses: actions/cache@v4
+        with:
+          path: ~/.bun/install/cache
+          key: ${{ runner.os }}-bun-${{ hashFiles('docs/bun.lockb') }}
+          restore-keys: |
+            ${{ runner.os }}-bun-
+      - name: Build documentation
+        run: bun run docs:build
+      - name: Deploy Github Pages
+        uses: peaceiris/actions-gh-pages@v4
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: docs/.vitepress/dist
+          force_orphan: true

docs/index.md

@@ -20,7 +20,7 @@ hero:
       text: GitHub
       link: https://github.com/amtoaer/bili-sync
   image:
-    src: /assets/icon.png
+    src: /logo.png
     alt: bili-sync
 
 features: