refactor: 重构设置、API、图库与存储页面前端结构。

将操作日志并入设置侧栏，补齐检查更新提示与版本接口刷新；拆分各模块组件并修复图库搜索分页变量。

app/components/api/ApiMethodBadge.vue

@@ -0,0 +1,34 @@
+<script setup lang="ts">
+import type { ApiDocMethod } from '~/composables/useApiDocs'
+
+const props = defineProps<{
+  method: ApiDocMethod
+  size?: 'xs' | 'sm'
+}>()
+
+const colorClass = computed(() => {
+  switch (props.method) {
+    case 'GET':
+      return 'bg-sky-500/15 text-sky-700 dark:text-sky-300'
+    case 'POST':
+      return 'bg-primary/15 text-primary'
+    case 'DELETE':
+      return 'bg-red-500/15 text-red-700 dark:text-red-300'
+    default:
+      return 'bg-muted text-muted'
+  }
+})
+
+const sizeClass = computed(() =>
+  props.size === 'sm' ? 'px-2 py-0.5 text-xs' : 'px-1.5 py-0.5 text-[10px]'
+)
+</script>
+
+<template>
+  <span
+    class="inline-flex shrink-0 rounded font-mono font-semibold leading-none"
+    :class="[colorClass, sizeClass]"
+  >
+    {{ method }}
+  </span>
+</template>