My first choice would be a new cane. Maybe you could
use a heavy-duty band clamp. Maybe 5-minute epoxy.
Another possibility might be to epoxy in a steel shaft
coming up from the bottom.

But I'm not sure any repair is realistic. A cane is
something you need to depend on. One collapse could
be very dangerous. If it were me I'd sacrifice the
aesthetic appeal of the home made cane and just make
sure I had a strong one.