It is called surging.
The mower runs short of fuel and starts to slow down so the governor opens the throttle wide and the engine picks up speed then the fuel level in the float bowl drops and the engine drops speed so the governor opens up the throttle again.
99,99% of the time is is because there is a blockage in the fuel supply.
Time to remove the carb and clean it , drain the fuel tank ( checking for water ) replace the fuel filter.
check the fuel tank for debris blocking off the fuel outlet.
There is a slim chance that the fuel pump is not working properly but most that get replaced are perfectly good as they rarely give problems.
I did everything but inspect the carb. Ordered a new one for $25. Cheap enough. Fuel pump works great. I saw the new fuel filter fill up when cranking it over after I drained all the old gas out of it.
It had 5 star reviews. Ive bought 2 different cheap carbs in the last 2 weeks for different machines and bolted them right on and never had a problem. Didnt even have to adjust them.I do hope it was an original one and not a cheap Chinese copy off evil pay.
A lot of the cheapies have been what Kohler & Briggs rejected as being below acceptiable quality standards.
I have had some problems with customers fitting them then refusing to believe their new carb was not working properly.