The generator is driven by a diesel engine. When an electrical appliance is connected, the internal coil of the generator and the external electrical appliance form a loop, which will generate current. When there is current, electromagnetic force resistance torque will be generated, and energy is conserved. For a generator with a stable speed, more electromagnetic resistance does more work, which means that the resistance torque is large.
When there is no electrical appliance, there is no current inside the generator coil, and the coil generates an electromagnetic resistance torque.
However, the bearing and belt of the generator will have resistance torque, which also consumes the power of the diesel engine. In addition, the diesel engine itself is a four-stroke, only one of which is a power stroke, and it also requires fuel consumption to maintain its idle operation. The efficiency of the diesel engine as a heat engine of an internal combustion engine is also limited.
When the generator power is large and the consumer power is small, these power losses may be larger than the consumer power. Diesel engine power is difficult to make small, so the minimum power of diesel generator is a few kilowatts. For a power tool of several hundred watts, this load is negligible. The above confirms what you said, with or without electrical appliances, the fuel consumption is similar.