Update task info before notifying task removal.

Ensure TaskViewTaskController updates task information before notifying
listeners of task removal. This prevents outdated information (e.g.,
windowing mode) from causing unintended cleanup behavior in consumers
like BubbleTaskView during bubble-to-fullscreen transitions.

Bug: 388630258
Flag: com.android.wm.shell.enable_create_any_bubble
Test: atest WMShellUnitTests:TaskViewTest
Change-Id: Iea8597c629647e874b8ff93e8bd50c093b45492e