Before I call out a plumber, I wanted to get a range of ideas for possible fixes. My 2" watching machine drain was backing up, so I tried to auger it with a handheld 1/4in handle-type auger. This is the small S-type handle auger with black plastic handles on each side of the body.

As I was drawing the cable out after my final attempt, the black plastic handle slipped off of the drain-facing side, and fell down to the trap of the pipe. I ride to spear it with a coat hanger, and flood the pipe with water so it would float to the top, but it seems like I've flooded it past the trap to an unknown distance down the drain.

If I were to call out a professional, do they have any pincer-type extensions at the end of drain cameras? Would the strategy be to push the plastic handle the rest of the way down the pipe? This is a slab foundation by the way