Looking from the outside, the crank threads seem to have worn. There are threads on approximately one third of the inner side. When the pedal is tightened, there is no movement. Should I risk taking the bike on a tour or change the whole crankset?

The threads can be repaired by insertion of a Helicoil insert; the threads will be stronger than new.

Riding around town? I'd be inclined to take my chances and leave it as is. Taking it on a tour? Replace the crankset (or crank arm) or repair it with a helicoil.

I took your advice and replaced the crankset. It would have been more expensive to fix it than buy a new one.

Thanks.