BasePlayerControl: Fix shuffle playlist mode de-sync

By removing shuffle mirroring property we now have only single source
of truth left for this data, and we won't end up with broken bindings
after manual assignments.

Fixes possible de-sync between the state of the Shuffle button and the
actual state in mediaPlayListProxyModel. It can be caused by clicking
on the button at least once, and then toggling the mode via global
application menu.