Hello M.,
Welcome to the forum.
We are all here to help when we can, but you need to include the build label information off of the chassis and the engine.
The mower manufacturer does not make the engines used on their riders; they buy them from engine builders through private contract agreements.
I watched your videos. My crystal ball says a worn-down cam lobe. Take the plugs out, remove the valve covers and turn the top of the engine fan by hand. Watch the valves carefully to see if they open about the same amount. If they do, there is not a cam problem.
Another possibility is "sticky" valves and guides from old fuel residue collecting on the valve stems. This is a very real problem with today's gasoline. There are just way too many additives in the gasoline that is focused on fuel injected automotive engines.
I happen to be working on a Kohler V-twin (similar design) at the moment that stuck both of the intake valves and bent the push rods. It was running fine the day before, then sat overnight and cooled. The next day, when cranked the valves were stuck solid in the valve guides.
To help prevent this issue, I recommend you pour a small amount of Marvel Mystery oil in the engine oil, then add some to the gasoline. About 1-ounce in each should work well. Run it and see if the problem clears up and the engine runs better. MM oil breaks down carbon and sludge buildup that is very common with air cooled engines.
By the way, throttling the engine up and down constantly can produce a slight backfire in the exhaust because the airflow in the intake is being disrupted. That causes excess fuel to puddle in the intake runners, then get sucked in all at once. The fuel travel through the cylinder and finally produces a backfire affect in the hot muffler.
Thought number 3 is the diodes on the ignition coil kill wire circuit are starting to go bad and allowing crossfire leakage/ firing one of the coils when it should not be. I've seen a lot of mowers scrapped before their time because of this misunderstood electrical design. This is usually suspect if it is running at a steady high speed and "pops" loudly in the exhaust on occasion.
Thought number 4 is one of the exhaust outlet gaskets are blown and sucking in cooler air when the engine is at high RPM.
That's all the possibilities I can come up with for now.