My current kitchen has a quite good vent that exhausts outside. Several years ago when I was testing a weather station with a particulate sensor before deploying it, it would pick up large spikes when I cooked, even though it was across the house and behind several doors. For air quality specifically, I very much doubt that realistic levels of separation between the kitchen and the rest of the house make much difference.

You can doubt it but it’s a fairly simple idea. Most homes don’t have makeup air systems. You have adequate ventilation you need makeup air. A good compromise is having an area that does not allow odors and smoke to move around easily. Hence separation. Now of course an adequate hood is the best but only the 1% of homes have that.

If you had all the windows closed and you don’t have makeup air, then running the exhaust will suck air in through any available gaps, which can potentially worsen air quality.

Try measuring PM2.5 in that room and log it as you turn on the fan for a while without cooking anything.