Plastic bags are made of polypropylene, and are garbage.

Plastic for the most part is basically garbage, there are so many types that it’s hard to recycle it. PET and HDPE can be recycled fairly easily if they’re sorted, the rest aren’t really worth it (polypropylene, low density polyethylene, PVC).

The only thing that is almost always economically worth recycling is metal, which is separated from the paper/glass/plastic if you have single stream recycling. Plastic should be burned in a cement kiln or buried in a modern landfill, unless it’s well sorted HDPE or PET.

If you recycle then it's probably just going to a street or ocean somewhere else. Plastic recycling is more or less made up.

They could go into a furnace to get turned into heat, electricity and CO2.

In theory yes, in practice they will be "exported" to a thrid world country with limited processing capabilities and directly dumped into the ocean.

Reuse is significantly more effective than recycling. Bothering is something we should indeed do. Though yes, disposing of bags properly is also much superior to just throwing them on the floor.

If you use single stream recycling for this, then this is actively bad. Plastic bags clog the sorting machines, and then get thrown out because (even if labeled) they are usually contaminated.