[SB][Screen Chips] Don't use DialogTransitionAnimator to launch dialogs

We were previously using the DialogTransitionAnimator to make a
beautiful animate-in animation when you tap on the chip -- the chip
gracefully turns into the dialog. But, this created some problems (see
linked bugs). This CL updates us to use the basic `dialog.show` instead.

Fixes: 350891338
Fixes: 347985465
Bug: 332662551
Flag: com.android.systemui.status_bar_screen_sharing_chips

Test: Start screen recording then stop -> verify that the chip doesn't
start using the wrong icon

Change-Id: I09deb7be96bf55a6e01315a7ede6a0b5623c7c41