[Handoff][6/N] Properly launch activity as current user

Because `OutboundHandoffRequestController` is running in `system_server`, `startActivity()` will not start as the current user. This change fixes that by manually starting the activity as the logged-in user.

Test: Validated manually, and updated unit tests with new calls
Bug: 400970610
Flag: android.companion.enable_task_continuity
Change-Id: Ic5a0241c9e764e905b2ae9231186c8bcab5b7fd7