Not sure what your gauge for bad is, but low-temperature burning of coal and wood, which is what you get with cheap wood heaters, produces smoke that is definitely polluting and unhealthy. You can get a wood burner that re-burns well and is very efficient and burns the smoke so completely that you mostly get CO2 and water vapor coming out of the chimney, but they're expensive.
Care to share more about trash burning? I'd be surprised if people living in Krakow or Warsaw commonly burn trash.
I was travelling a lot a couple of days ago across the countryside just outside of Krakow, and people are definitely burning plastics and trash, you can smell it even inside your car in the early hours of the morning.
It's coming from the surrounding areas, not the city itself.
Since 2019 people living in Krakow do not burn any solids for heating, because the city introduced total ban on solid fuels including coal and wood an the ban is quite effective.
But people around the city and, frankly, in most of Poland still burn solid fuels and if you drive around these places the smell can be really terrible and the smoke color and density coming from some chimneys definitely doesn't look like a dry wood smoke. Such smoke is often a product of burning very low quality, super fine-grained coal or rather coal dust, which is the cheapest fuel available.
Btw, you can burn plastic just fine in a proper industrial incinerator.
It's people from surrounding areas who are experiencing energy poverty. City buildings typically have either central heating or gas furnaces.
A common sight in my area at this time of the year is a senior person driving up to a community dumpster in an equally old car with plates indicating not being from around here and looking for loose pieces of wood - typically furniture.
The sale of furnaces that would even fit something like this for burning was banned in IIRC 2018, but there's a backlog of still functioning ones that are used.
Anyone trying this in a city would have the authorities called on them, but deep in rural areas few care.