feat(splashscreen): enhance startup sequence and splashscreen handling

This update improves the splashscreen management during application startup. The splashscreen will now remain visible for a minimum duration and will only close after the main application is ready, ensuring a smoother user experience.

- Introduced a new startup sequence to manage background tasks.
- Added error handling for splashscreen closure to maintain functionality.
- Optimized the timing for displaying and hiding the splashscreen.

src/App.svelte

@@ -1,5 +1,6 @@
 <script lang="ts">
   import { onDestroy, onMount, tick } from "svelte";
+  import { invoke } from "@tauri-apps/api/core";
   import { open as openDialog } from "@tauri-apps/plugin-dialog";
   import { check, type DownloadEvent, type Update } from "@tauri-apps/plugin-updater";
   import { AlertCircle, BookOpen, Cherry, Download, FolderOpen, GitBranch, GitMerge, LoaderCircle, Plus, Search, Star, X } from "@lucide/svelte";
@@ -268,6 +269,8 @@
   const BACKGROUND_FETCH_INTERVAL = 180_000;
   const BACKGROUND_FETCH_AFTER_SWITCH_GRACE_MS = 30_000;
   const BACKGROUND_FETCH_OTHER_BATCH_SIZE = 2;
+  const STARTUP_SPLASH_MIN_VISIBLE_MS = 850;
+  const STARTUP_FETCH_MAX_WAIT_MS = 20_000;
   let backgroundFetchTimer: ReturnType<typeof setInterval> | undefined;
   let backgroundRepoStatusTimer: ReturnType<typeof setInterval> | undefined;
   let backgroundFetchInFlight = false;
@@ -346,14 +349,7 @@
   // ── Lifecycle ──────────────────────────────────────────────────────────────
 
   onMount(() => {
-    initAnalytics();
-    loadRepoLists();
-    autoRefreshTimer = setInterval(() => { void autoRefreshTick(); }, AUTO_REFRESH_INTERVAL);
-    backgroundRepoStatusTimer = setInterval(() => { void backgroundRepoStatusTick(false); }, BACKGROUND_REPO_STATUS_INTERVAL);
-    backgroundFetchTimer = setInterval(() => { void backgroundFetchTick(); }, BACKGROUND_FETCH_INTERVAL);
-    void backgroundRepoStatusTick(false);
-    void checkForUpdates();
-    void initCommitAi();
+    void runStartupSequence();
   });
 
   onDestroy(() => {
@@ -368,6 +364,96 @@
     if (activeFileHistoryRequestId) void cancelFileHistory(activeFileHistoryRequestId);
   });
 
+  function wait(ms: number): Promise<void> {
+    return new Promise((resolve) => window.setTimeout(resolve, ms));
+  }
+
+  function waitForAnimationFrame(): Promise<void> {
+    return new Promise((resolve) => requestAnimationFrame(() => resolve()));
+  }
+
+  async function waitForStartupPaint() {
+    await tick();
+    await waitForAnimationFrame();
+    await waitForAnimationFrame();
+  }
+
+  async function closeStartupSplashscreen() {
+    try {
+      await invoke("close_splashscreen");
+    } catch {
+      // Browser preview and failed startup paths should keep working without Tauri.
+    }
+  }
+
+  function startBackgroundTimers() {
+    autoRefreshTimer = setInterval(() => { void autoRefreshTick(); }, AUTO_REFRESH_INTERVAL);
+    backgroundRepoStatusTimer = setInterval(() => { void backgroundRepoStatusTick(false); }, BACKGROUND_REPO_STATUS_INTERVAL);
+    backgroundFetchTimer = setInterval(() => { void backgroundFetchTick(); }, BACKGROUND_FETCH_INTERVAL);
+  }
+
+  async function runStartupSequence() {
+    const startupStartedAt = performance.now();
+
+    initAnalytics();
+    loadRepoLists();
+
+    void checkForUpdates();
+    void initCommitAi();
+
+    try {
+      await waitForStartupPaint();
+      await Promise.race([
+        fetchOpenRepositoriesDuringStartup(),
+        wait(STARTUP_FETCH_MAX_WAIT_MS),
+      ]);
+    } finally {
+      const remainingSplashTime = STARTUP_SPLASH_MIN_VISIBLE_MS - (performance.now() - startupStartedAt);
+      if (remainingSplashTime > 0) await wait(remainingSplashTime);
+
+      await closeStartupSplashscreen();
+      startBackgroundTimers();
+      void backgroundRepoStatusTick(false);
+    }
+  }
+
+  async function fetchOpenRepositoriesDuringStartup() {
+    const paths = uniqueRepoPaths(repoTabs.map((tab) => tab.path));
+    if (paths.length === 0 || backgroundFetchInFlight) return;
+
+    let fetchedRepositories = 0;
+    let failedRepositories = 0;
+    backgroundFetchInFlight = true;
+    trackEvent("startup_open_repositories_fetch_started", {
+      open_repositories: paths.length,
+    });
+
+    try {
+      for (const path of paths) {
+        try {
+          const nextStatus = await fetchRemote(path);
+          if (sameRepoPath(path, activeRepoPath)) applyStatus(nextStatus);
+          else updateRepoManagementStatus(path, nextStatus);
+          fetchedRepositories += 1;
+        } catch {
+          failedRepositories += 1;
+          try {
+            updateRepoManagementStatus(path, await getStatus(path));
+          } catch {
+            // Keep the cached tab data if this repo is unavailable at startup.
+          }
+        }
+      }
+    } finally {
+      backgroundFetchInFlight = false;
+      trackEvent("startup_open_repositories_fetch_finished", {
+        open_repositories: paths.length,
+        fetched_repositories: fetchedRepositories,
+        failed_repositories: failedRepositories,
+      });
+    }
+  }
+
   $: scheduleAutoHideError("errorMessage", errorMessage, (message) => {
     if (errorMessage === message) errorMessage = "";
   });