If they rate a gen at 4000W continuous, that is usually the 240V rating that they are giving (unless it has a switchable 120V only mode).If the gen is rated to 4000w running load - that comes out to 33.333 amps, or 66% over the breaker rating, or 166% of the breaker rating.
By that math - it would counter your theory that a breaker should break at 145% - the gen's running wattage would be 21% beyond that 145% number.
So if that is the case - again, the breaker should be the weak point. Instead, the inverter faulted.
But your gen is rated at 5500W (on gasoline) so that gives 5500 / 2 = 2750W (22.9A) available at the 120V receptacles. However, they put 20A breakers on those receptacles. In terms of percentage, 22.9A is only 114% of the breaker rating of 20A.
However, I don't think the breaker is your issue as it is not tripping. The inverter is able to control the output current much faster than the breaker can react to your welder. The surge demand of the welder at the 110A output is pushing the inverter faster to overload quicker than the breaker reacts. Apparently, that particular load puts the gen just right at the point of either the breaker or the inverter tripping out. In this case, it is the inverter that is beating the breaker.
On some gens they don't even use a breaker on the highest capacity receptacle on the panel. They just let the inverter do the work of limiting the output at the receptacle. My gen is like that.