Briggs? There's your problem. You'll need to replace it with a Kohler and all will be well...... Lol Although, I am partial to Kohler. I put them through the paces...... One of the recommendations above should fix the issue.... I believe when my pusher did that it was the filter....
Surging is usually (not always) caused by the carburetor jet(s) becoming clogged. It causes a lean running condition and the governor on the engine (which most power equipment engines have) constantly is searching to adjust.
you can sort of test this out if you have a choke on the engine . . . give it a little bit of choke and see if it stops surging. If so, then run a high concentration of carburetor (or fuel injector) cleaner to the gas and run for a bit. Of course that may be something for next season.
That plastic carb fuel pick up tube that goes into the gas tank has a little screen in the bottom....it's plugged with debris....just clean it and your surging will stop
I'd like to know how it went too . When my lawnmower had the idle surge, it was a dirty air filter. I have to clean mine 3-4 times per season. I had to rebuild the carb on my chainsaw last year and it was easy. After you've rebuild boat carbs, a small engine carburetor is a piece of cake