Engine surging is 99.9 % of the time caused by the mixture being too lean to maintain a constant speed.
Speed drops, governor allows throttle to open fully which causes the carb to "suck" harder on the main jet on the initial increase in the air.
This causes more volume of fuel to be sucked into the engine so the governor closes down the throttle the "suck" becomes less and the mixture becomes too weak so the governor allows the throttle plate to open up again.
Thus the cycle continues .
Common Causes
float bowl fuel level too low
Bowl vent hole blocked or obstructed
insufficient fuel supply to the carb
badly worn carb allowing air to enter around the throttle plate shaft ( common on older engines )
Main jet too small
Air leak between the main jet & the inlet valve
Some repair shops are a lot better than others and if attached to a glass fromt new mower shop their main objective is to convince you your old mower needs to be replaced by one of their new mowers .