Make mutable state flow in the bind function scope

Since the binder self is a singleton, we should always create a new
mutable state flow for the heights of the toolbar components.

Test: Manually tested. See bug.
Bug: 394739225
Flag: com.android.systemui.shared.new_customization_picker_ui
Change-Id: Iedaf058dbfa58bc54681e354300362935b8c7665