Fix grid screen options (2/2)

Do the following measures to avoid too many unnecessary emits of data
1. Make data flow shared
2. Make state flow lazily emit

Test: Made sure that the data flow emit only necessary data
Bug: 362237825
Flag: com.android.systemui.shared.new_customization_picker_ui
Change-Id: I23026c83412d2f2a7b20a808c9bab943affdb4fc