Whether or not an airline will pay for a hotel room has nothing to do with whether or not you have "Easyjet Plus" or any other type of ticket or product sold by the airline.

When an airline is legally obliged to pay for a hotel, and if it is not convenient or easy to get the airline to rebook you in situ, it is usually sufficient to make and pay for your own booking and submit a claim after the fact; as long as the cost is reasonable (which, of course, can vary by circumstance and airline) they should refund you.

I know of no airline that will "move you to a flight later that same day if it is full" - standard practice is that people that hold confirmed bookings on operating flights will be accommodated. (Moving people from other/earlier flights to a later flight, thereby displacing other customers, is basically just playing "musical chairs" and increasing disruption).