Handle SDKContextClass client initialisation internally (#34146)

* Handle SDKContextClass `client` initialisation internally

Rather than via MatrixChat - this is predominantly for Lifecycle tests as they don't use a MatrixChat and it doesn't make much sense for this component to own this state.

* Fix tests

apps/web/test/unit-tests/stores/widgets/WidgetPermissionStore-test.ts

@@ -54,7 +54,7 @@ describe("WidgetPermissionStore", () => {
         );
         mockClient = stubClient();
         const context = new TestSDKContext();
-        context.client = mockClient;
+        context._client = mockClient;
         widgetPermissionStore = new WidgetPermissionStore(context);
     });