Fix widgets getting stuck in loading states (#31314)

* Refer to ClientWidgetApi as "widget API" rather than "messaging"

* Rename StopGapWidgetDriver to ElementWidgetDriver

* Rename StopGapWidget to WidgetMessaging

* Fix WidgetMessaging's lifetime by storing it in WidgetMessagingStore

(Rather than storing just the raw ClientWidgetApi objects.)

* Unfail test

* use an error

* cleanup start

* Add docs

* Prettier

* link to store

* remove a let

* More logging, split up loop

* Add a test demonstrating a regression in Call.start

* Restore Call.start to a single, robust event loop

* Fix test failure by resetting the messaging store

* Expand on the WidgetMessaging doc comment

* Add additional tests to buff up coverage

* Add a test for the sticker picker opening the IM.

* reduce copy paste

---------

Co-authored-by: Half-Shot <will@half-shot.uk>
Co-authored-by: Timo K <toger5@hotmail.de>

test/unit-tests/components/views/rooms/RoomTile-test.tsx

@@ -20,7 +20,6 @@ import {
 import { KnownMembership } from "matrix-js-sdk/src/types";
 import { Widget } from "matrix-widget-api";
 
-import type { ClientWidgetApi } from "matrix-widget-api";
 import {
     stubClient,
     mkRoomMember,
@@ -47,6 +46,7 @@ import { MessagePreviewStore } from "../../../../../src/stores/room-list/Message
 import { MatrixClientPeg } from "../../../../../src/MatrixClientPeg";
 import SettingsStore from "../../../../../src/settings/SettingsStore";
 import { ConnectionState } from "../../../../../src/models/Call";
+import { type WidgetMessaging } from "../../../../../src/stores/widgets/WidgetMessaging";
 
 jest.mock("../../../../../src/customisations/helpers/UIComponents", () => ({
     shouldShowComponent: jest.fn(),
@@ -204,7 +204,7 @@ describe("RoomTile", () => {
                 widget = new Widget(call.widget);
                 WidgetMessagingStore.instance.storeMessaging(widget, room.roomId, {
                     stop: () => {},
-                } as unknown as ClientWidgetApi);
+                } as unknown as WidgetMessaging);
             });
 
             afterEach(() => {