fix(app): keep tablet sidebar controls above system navigation (#7768)

The wide sidebar reserved only the top safe area, leaving its footer under Android navigation UI. Apply the existing bottom inset to the same interior and add a native geometry regression check.

Co-authored-by: paseo-bot[bot] <266920839+paseo-bot[bot]@users.noreply.github.com>

packages/app/e2e/mobile/sidebar-system-insets/android.mjs

@@ -0,0 +1,40 @@
+// Open a connected host with the wide sidebar visible, keyboard closed, and
+// three-button navigation enabled on an Android tablet. Run against a fresh build:
+// node packages/app/e2e/mobile/sidebar-system-insets/android.mjs <session> <adb-serial>
+import assert from "node:assert/strict";
+import { execFileSync } from "node:child_process";
+
+const [, , session, serial] = process.argv;
+assert(session && serial, "Pass the agent-device session and adb serial");
+const windowState = execFileSync("adb", ["-s", serial, "shell", "dumpsys", "window"], {
+  encoding: "utf8",
+  timeout: 10_000,
+});
+const navBar = windowState.match(/type=navigationBars frame=\[0,(\d+)\]\[\d+,\d+\] visible=true/);
+assert(navBar, "A visible bottom navigation bar is required");
+assert(!/type=ime .*visible=true/.test(windowState), "Close the keyboard first");
+const navigationTop = Number(navBar[1]);
+const { data } = JSON.parse(
+  execFileSync("agent-device", ["snapshot", "--raw", "--json", "--session", session], {
+    encoding: "utf8",
+    timeout: 60_000,
+  }),
+);
+const focusedApp = windowState.match(/mCurrentFocus=.*? u\d+ ([^/\s]+)\//)?.[1];
+assert.equal(
+  focusedApp,
+  data.appBundleId,
+  "Snapshot must belong to the focused app on this device",
+);
+for (const id of [
+  "sidebar-add-project",
+  "sidebar-hosts-trigger",
+  "sidebar-help",
+  "sidebar-settings",
+]) {
+  const button = data.nodes.find((node) => node.identifier === id);
+  assert(button?.rect, `${id} must be visible above the system navigation bar`);
+  const bottom = button.rect.y + button.rect.height;
+  assert(bottom <= navigationTop, `${id} ends at ${bottom}, below navigation top ${navigationTop}`);
+  console.log(`PASS: ${id} bottom=${bottom}, navigationTop=${navigationTop}`);
+}

packages/app/src/components/left-sidebar.tsx

@@ -719,8 +719,11 @@ function DesktopSidebar({
     [active, resizeAnimatedStyle],
   );
   const desktopSidebarBorderStyle = useMemo(
-    () => [styles.desktopSidebarBorder, { flex: 1, paddingTop: insetsTop }],
-    [insetsTop],
+    () => [
+      styles.desktopSidebarBorder,
+      { flex: 1, paddingTop: insetsTop, paddingBottom: insets.bottom },
+    ],
+    [insetsTop, insets.bottom],
   );
   const sidebarHeaderGroupStyle = useMemo(
     () => [styles.sidebarHeaderGroup, ownsTopLeft && styles.sidebarHeaderGroupBelowChrome],