Refactor: Add library stats, server info, and helper utilities

Extract more reusable components and utilities:

Components:
- PlexLibraryStats.vue: 4-card stats grid with loading states
- PlexServerInfo.vue: Server details and sync/unlink actions

Composables:
- usePlexLibraries.ts: Library data loading and processing logic

Utilities:
- plexHelpers.ts: Pure functions for formatting and calculations
  - getLibraryIcon/Title: Type to display mapping
  - formatDate/MemberSince: Date formatting
  - processLibraryItem: Parse API response to display format
  - calculateGenreStats: Top 5 genres from metadata
  - calculateDuration: Total hours, episodes, tracks

Benefits:
- Cleaner separation: UI vs logic vs utilities
- Testable pure functions
- Reusable across components
- Reduces PlexSettings.vue complexity

src/composables/usePlexLibraries.ts

@@ -0,0 +1,120 @@
+import { ref } from "vue";
+import { usePlexApi } from "./usePlexApi";
+import {
+  processLibraryItem,
+  calculateGenreStats,
+  calculateDuration
+} from "@/utils/plexHelpers";
+
+export function usePlexLibraries() {
+  const { plexServerUrl, fetchLibrarySections, fetchLibraryDetails } =
+    usePlexApi();
+
+  const loading = ref(false);
+  const libraryStats = ref({
+    movies: 0,
+    shows: 0,
+    music: 0,
+    watchtime: 0
+  });
+
+  const libraryDetails = ref<any>({
+    movies: {
+      total: 0,
+      recentlyAdded: [],
+      genres: [],
+      totalDuration: "0 hours"
+    },
+    shows: {
+      total: 0,
+      recentlyAdded: [],
+      genres: [],
+      totalEpisodes: 0,
+      totalDuration: "0 hours"
+    },
+    music: { total: 0, recentlyAdded: [], genres: [], totalTracks: 0 }
+  });
+
+  async function loadLibraries(authToken: string) {
+    loading.value = true;
+
+    // Reset stats
+    libraryStats.value = { movies: 0, shows: 0, music: 0, watchtime: 0 };
+
+    try {
+      const sections = await fetchLibrarySections(authToken);
+
+      for (const section of sections) {
+        const type = section.type;
+        const key = section.key;
+
+        if (type === "movie") {
+          await processLibrarySection(authToken, key, "movies");
+        } else if (type === "show") {
+          await processLibrarySection(authToken, key, "shows");
+        } else if (type === "artist") {
+          await processLibrarySection(authToken, key, "music");
+        }
+      }
+    } catch (error) {
+      console.error("[PlexLibraries] Error loading libraries:", error);
+      throw error;
+    } finally {
+      loading.value = false;
+    }
+  }
+
+  async function processLibrarySection(
+    authToken: string,
+    sectionKey: string,
+    libraryType: string
+  ) {
+    try {
+      const data = await fetchLibraryDetails(authToken, sectionKey);
+      if (!data) return;
+
+      const totalCount = data.all.MediaContainer?.size || 0;
+
+      // Update stats
+      if (libraryType === "movies") {
+        libraryStats.value.movies += totalCount;
+      } else if (libraryType === "shows") {
+        libraryStats.value.shows += totalCount;
+      } else if (libraryType === "music") {
+        libraryStats.value.music += totalCount;
+      }
+
+      // Process recently added items
+      const recentItems = data.recentMetadata
+        .slice(0, 5)
+        .map((item: any) =>
+          processLibraryItem(item, libraryType, authToken, plexServerUrl.value)
+        );
+
+      // Calculate stats
+      const genres = calculateGenreStats(data.metadata);
+      const durations = calculateDuration(data.metadata, libraryType);
+
+      // Update library details
+      libraryDetails.value[libraryType] = {
+        total: totalCount,
+        recentlyAdded: recentItems,
+        genres,
+        totalDuration: durations.totalDuration,
+        ...(libraryType === "shows" && {
+          totalEpisodes: durations.totalEpisodes
+        }),
+        ...(libraryType === "music" && { totalTracks: durations.totalTracks })
+      };
+    } catch (error) {
+      console.error(`[PlexLibraries] Error processing ${libraryType}:`, error);
+    }
+  }
+
+  return {
+    loading,
+    libraryStats,
+    libraryDetails,
+    loadLibraries
+  };
+}