Reroute Manage Windows open instance transition through shell transition

Prevents a crash in non-desktop Manage Windows by routing the task start
through StageCoordinator instead of SplitScreenController, the former of which uses shell transition.

Bug: 392053741
Test: Manual
Flag: com.android.window.flags.enable_desktop_windowing_multi_instance_features
Change-Id: Ibf24f09f18defb1b9af45cbc306771287ebcc0e9