What will be the steady state Charge distribution of given configuration- battery vs capacitor
The battery makes as much charge as it needs, using chemistry, to keep the plate potential the same: you may say “voltage is conserved”.  In the capacitor situation charge is conserved, voltage is not.
So when the switch is closed, the charge stays the same, the voltage is less, in the capacitor case.  In the battery case, more charge is made and the voltage stays the same.