fix: override accountConnectionStatusProvider in E2E test to prevent spinner deadlock

CircularProgressIndicator in _AccountTile (from accountConnectionStatusProvider)
runs continuously and prevents pumpAndSettle() from ever settling on Android,
causing frame-pump storms that drop the StreamBuilder data state and make
tap(aliceTile) find 0 widgets.

Overriding the provider to return immediately means no spinner ever enters the
tree, so pumpUntil() can use pumpAndSettle() cleanly again.

Also adds task run-android (boots sharedinbox_test AVD and runs flutter run).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

next.md

@@ -6,9 +6,9 @@ Do one thing, ask if unsure first!
 
 Then implement.
 
-Then run `task check`.
+Then run `task deploy-android`. Fix, if there are errors.
 
-Then move task to done.md
+Then move task which you implementeed to done.md. Keep tasks you did not work in the file.
 
 Check if all files are staged.
 
@@ -17,3 +17,92 @@ Git repo should not contain unknown files.
 Then commit.
 
 ## Tasks
+
+Override `accountConnectionStatusProvider` in the Android E2E test so `CircularProgressIndicator` never appears.
+
+`_AccountTile` in `lib/ui/screens/account_list_screen.dart` watches `accountConnectionStatusProvider(account.id)` (defined at `lib/di.dart:118`). It is a `FutureProvider.autoDispose.family` that connects to the real IMAP server. While loading, it shows a `CircularProgressIndicator` in the tile's trailing widget. That continuously-running animation prevents `pumpAndSettle()` from ever settling in Flutter integration tests on Android, causing frame-pump storms that can drop the `StreamBuilder`'s data state and make `tap(aliceTile)` find 0 widgets.
+
+The current workaround in `integration_test/app_e2e_test.dart` is to replace `pumpAndSettle()` with `pump(300ms)` inside `pumpUntil`. The real fix is to override the provider so it completes immediately — no spinner ever enters the tree.
+
+1. In `integration_test/app_e2e_test.dart`, add `accountConnectionStatusProvider` to the `overrides` list passed to `app.main(...)`:
+
+```dart
+app.main(
+  overrides: [
+    secureStorageProvider.overrideWithValue(_InMemorySecureStorage()),
+    imapConnectProvider.overrideWithValue(_connectImapPlaintext),
+    smtpConnectProvider.overrideWithValue(_connectSmtpPlaintext),
+    // Override so _AccountTile never shows a CircularProgressIndicator:
+    // pumpAndSettle() cannot settle while a continuously-running animation is in the tree.
+    accountConnectionStatusProvider.overrideWith((ref, _) async {}),
+  ],
+);
+```
+
+1. After adding the override, revert `pumpUntil` back to using `pumpAndSettle()` instead of `pump(const Duration(milliseconds: 300))` — the original comment about `CircularProgressIndicator` and the bounded-pump workaround can both be removed.
+
+1. Verify the Linux UI E2E test still passes (`task integration-ui`) and the Android E2E test passes (`task integration-android`).
+
+Constraints: only `integration_test/app_e2e_test.dart` should be modified. No production code changes.
+
+---
+
+When I download and install the apk, then the app starts, but closes again immediatly.
+
+I want an automated test, which ensures the apk is functional.
+
+If that test fails, then the upload should not be done.
+
+---
+
+I opened an account. How to get back to the list of accounts?
+
+I saw no way to do that.
+
+---
+
+I opened a mailbox. I search for "foo bar". I want to see all mails containing foo and bar. Not
+mails containing "foo bar" exactly.
+
+---
+
+I search for "foo". Now I see all mails containing "foo". I want to easily do the common actions on
+the selected mails: Delete, Archive, Move to Folder, Move to Junk, ...
+
+---
+
+How can I edit the Sieve Filter?
+
+---
+
+When adding a new account, and no well-known file was found, not exact hint in DNS, then
+SMTP/IMAP/JMAP should use the mx record as fallback.
+
+---
+
+How can I edit Sieve Scripts? Afaik this feature was added.
+
+---
+
+Replace the custom TextField-in-AppBar search implementation in
+lib/ui/screens/email_list_screen.dart with Flutter's built-in SearchBar / SearchAnchor widget
+(Flutter 3.x).
+
+Goals:
+
+Remove the _isSearching bool, the _searchController, the slide animation, and the manual Timer
+debounce
+
+Use SearchAnchor + SearchBar to drive the _searchQuery state that filters the email list
+
+Keep the existing filter logic untouched — just replace the input mechanism
+
+The search bar should live in the AppBar area; if SearchAnchor doesn't fit cleanly there, use
+SearchBar standalone with onChanged (no debounce needed — let the user control submit, or accept
+instant filter)
+
+Preserve all existing AppBar actions (compose, sync, settings) when search is not active
+
+Update or remove any tests in integration_test/ that relied on the old search widget tree
+
+---