The Russian interior minister said something along the lines that Putin should declare that the recognition of the breakaway republics refers to all of Donbass, not just the 1/3 the separatists hold. I’m not sure what exactly he has recognized. The separatists legally claim the entire two provinces, not just what they hold.
The next step will probably be an order to Ukrainian military and government forces to evacuate from all of the “independent” Donbass, followed by an attack on the Ukrainian lines if they don’t.
If there is military resistance by Ukraine, then that’s the point I’m guessing that Putin invades Ukraine as a whole and takes Kiev.
Putin has declared a no-fly zone over the Sea of Azov.
I think your scenario is quite likely.