My shop vac measures an average of 1300w. I would not run two of them off a single circuit.
I've also been suspicious of those tool / vac auto start devices and vacuums that have them built it. I would not plug something like a miter saw into them and the combined load is likely not safe for a single circuit.
Specs on the Fosman say..
Single 125VAC outlet - 15A Max
125VAC, 60HZ, 15A, Resistive
125VAC, 60HZ, 15A, General purpose
125VAC, 60HZ, 10A / 1250W,Tungsten
125VAC, 60HZ, 1/2HP TV-5
Which to me reads like a lot of chinesium.
The other day, I was assuming the Fosman had some kind of small relay inside it and today I realized that, that was a silly thought. It is much more likely to be using some kind of mosfet or IGBT to switch the power.