There can be a big difference between watts and "VA" ratings in some types of equipment; also power consumption labels may be worst case, rather than continuous consumption.
If the nebuliser has either a motor or a simple transformer rectifier power supply, the "power factor", how well the current taken lines up with the instantaneous voltage through each AC cycle, may be poor, meaning the current * voltage wattage does not equal the "VA" power it consumes.
Or it could just need less power than the label says..
Your meter appears to have a "Power factor" display - have a look at that?
A pure resistive load will (or should) have a power factor of 1, it behaves as you would expect with current proportional to voltage.
Anything reactive (capacitive or inductive) will have a lower power factor; the instantaneous current * voltage is somewhat higher than what you get by multiplying independently measured current and voltage as the current is not in step with the voltage.
More info:
https://circuitdigest.com/tutorial/what-is-power-factor-and-how-it-affects-your-energy-bills
Also note that with anything that takes a switch-on surge like a motor or PSU that has to charge up, the inverter must be big enough to take that without overloading and shutting down.
Normal power systems and fuses can take quite high surges for such things without any noticable effect, but inverters will often trip far faster and not take a load that is apparently OK for them.