PA-34-200T Flight Instructor reported failure to verify landing gear down resulted in a gear up landing and loss of control on the ground.

Narrative

I wanted to provide a statement on the incident that occurred during a checkride prep flight.I was acting as the MEI with my student; and we departed ZZZ past XA00. We began with a short-field takeoff; followed by a short-field landing to a full stop. After taking off again; we performed a simulated engine failure at 500 feet and returned to land single-engine. Following this; we departed once more to conduct a single-engine instrument approach.We attempted the RNAV XX approach with a circle-to-land for Runway XY. Approximately 0.3 miles from ZZZZZ; I simulated an engine failure. The student went through the appropriate drill and broke off the approach at 800 feet. While circling to join the downwind; the student completed the securing checklist and delayed the GUMPS checklist until reaching abeam the numbers. At that point; the GUMPS checklist was completed; and the student called out 'gear down; three greens; and one in the mirror;' though later mentioned that they could not see the mirror confirmation due to darkness. I visually confirmed three green indications. The student then extended 10 degrees of flaps.On the base leg; the student completed the GUMPS checklist again; called 'gear down; three greens;' and I confirmed. Flaps were extended to 25 degrees. On final; the student called out 'Red; Blue; Green; Gear down; three greens' to verify the gear status. Given the night conditions; I remained on the controls to assist with the landing if necessary.The final approach was stabilized at Vyse; with the left engine at zero thrust. Over the runway; the aircraft floated longer than usual at idle power. Shortly after touchdown; I heard a skidding noise. Unsure of the source or severity; I took control and initially attempted to go-around to check and cycle the gear. However; realizing that the safest option was to keep the aircraft on the ground due to the unknown extent of any damage; I immediately pulled the power to idle and cut the mixture. The aircraft came to a complete stop; at which point we heard the gear warning horn chirping.During the approach and landing; there were no abnormal aural or visual indications inside the cockpit. No throttle switch or flap switch gear down warning was heard; although the power did come to idle.After securing the aircraft; I stepped outside while leaving the master switches on to keep the lights illuminated. My student remained inside the plane to transmit on the comms; advising other traffic to avoid attempting to land on Runway XY and announcing that the airport was closed.