DocsUI: Try to fix a race condition in the test

The current approach of `waitForIdleSync()` doesn't seem to be enough
to avoid the race condition, trying another approach.

Bug: 397436065
Test: atest  DocumentsUIGoogleTests:com.android.documentsui.DialogUiTest
Flag: EXEMPT test fix
Change-Id: If01e64da2c2ee322d86631d16a78d818c4b67c8d