From what I’ve read the same indoor pollution exists with induction even if not vented. The confounding variable is that induction generally is present in new construction which will have proper ventilation.
One of the concerns is nitrogen oxides (mostly nitrogen dioxide, as I recall) from high temperature combustion. Car engines attempt to limit combustion temperatures (usually by adding some exhaust gasses to the intake air) to reduce its production.
Ventilation prevents it from reaching hazardous levels from a gas stove; induction does not produce it.
The point is most of the harm comes from the cooking, not the gas. Classic over optimizing. Might as well ban Teflon while you’re at it (the eu did this, as it’s harmful)
I'm not sure whether that's true (nitrogen dioxide can be pretty bad), but I am sure that ventilation is the answer either way. I suspect the main motivation for the ban is to be able to shut down the gas lines in the future because their existence results in methane leaking into the atmosphere. Health concerns might help them sell it ("think of the children" tends to be pretty effective, politically).
There is some evidence that the skyrocketing asthma rates are due to natural gas.
They should ban teflon. It leaches estrogen analogues into food, and is an endocrine disrupter. Also, teflon pans last 2-5% as long as cheaper cast iron / stainless steel equivalents (or most more expensive options).
Cooking on induction at moderate temperature does not seem to produce significant particulate pollution. Source: I have a stove, and I have a portable PM2.5 meter.
So you can simmer a stock for a couple hours without needing to run the fan (and cook most anything under 300 degrees or so), and with the fan off you don’t lose nice conditioned air from inside.
I don't have a view either way, but we can measure pollution from different cooking methods under controlled conditions so we know which is better or worse independent of ventilation.
Ventilation depends partly on individual behaviour, eg I open windows in good weather and close them in winter.
TLDR: it’s a function of ventilation