Over cranking a generator and another question

How bad is this? I was doing my regular test I do every few months on my generator so it doesn’t sit around idle for too long and was also doing some load tests on some new appliances it will need to run.

It’s a champion 2000 watt inverter briefcase generator if that adds any needed context. I was testing out the eco mode and some other features. When my portable AC fires up I can hear the generator really fire up. When eco mode was on, it caused my tv and all my other electronics to turn off then back on. I assume something with automatically switching off of eco mode to run the AC causes the circuit to temporarily break. No big deal for a fridge or something like that but for a television/computers clearly that interruption in power was enough to cause them to interrupt their operability. I tried turning eco mode off from the start and when the generator cranked up for the AC coming online the other electronics seemed to hold steady. Any thoughts on eco mode and how I should use it on this generator?

Also when I was firing it up after turning it off too quickly (the fuel valve and automatic shutoff are the same switch so I have to carefully shut the fuel off without turning it all the way so it bleeds the lines if any gas stuck in the system) and I had to crank it more than normal. Apparently the issue was I had it choked but I guess there was gas still in the system or something and it wouldn’t start until I totally opened the choke before I cranked it.

If I over crank the generator, what happens? Can it damage it to the point where I’ll need to go in and clean out the carburetor or worse have to take it and get it fixed?