Gas stoves fill the air in your home with particulate matter (pm), which has been found to increase cancer risk in the long term.
So next time you buy a stove, consider choosing an induction stove.
Btw, gas stoves being better or faster than induction is a myth. They have certain specific advantages, but they are actually slower.
Obligatory Technology Connections video:
https://www.youtube.com/watch?v=eUywI8YGy0Y
Very few residences have proper ventilation. In the US, a microwave above the stove is common. Microwave often do have a fan function, but the vast majority don’t vent outdoors. I doubt that running air through a very thin filter will do much good.