Wattage of adapter to size my inverter
The adapter's current will be largest at 100 V, not 240 V, the 1.5 A doesn't apply at all voltages.
Then for a low power device like this, the power factor is probably quite poor, maybe as low as 0.7, I guess. This means the current will be 1.4 x what you'd expect from the power. The inverter still has to supply this current.
Then the efficiency of the adapter is probably only 80%.
This still leaves a factor of two which can't be explained.
At 240 V, you can probably consider the steady state fully loaded current to be under 0.5 A, or 100 VA.
The inrush current when it is first connected, could be a lot higher, but inverters usually handle this with a brief voltage drop.
By the way, small inverters are notoriously overstated in their power ability. I have a cheap 120 watt inverter which can't power a laptop. You can see it in the price range, you can pay $25 or $250 for a 200 watt inverter, depending on how serious your application is.