For that matter, it's probably a net positive to put most plastic "recycling" into such schemes, as we're just turning plastic products into lower and lower grade pieces, with the associated generation of microplastics.
Nordics countries generally need lot of heating because of cold climate, which in cities is typically district heating, i.e. delivering the heat as hot water from big heating plants. Heat pumps are also very popular (air-to-air, air-to-water, geothermal).
For example, my house is entirely heated with 3 heat pumps, even in -25°C. From April to September 10 kW solar panels provide the most of energy, also charging my Tesla.
There's complicated interactions though, removing the plastics can affect the makeup of the fuel and the post combustion products can free recyclable metal from other materials they were combined with. Recycling processes often have an unrecyclable fraction which can be burned etc.
Waste -> district heating is definitely happening in Sweden. Probably more so than waste -> electricity. There are better ways to generate electricity and we need heating anyway big part of the season.