The sole is the problem, it is probably a version of nylon. On some of these plastics the fastest way to test is a burn test, actually you melt a wee bit and smell the smoke, obviously don't inhale the stuff.
Bonding to nylon is a chore, 3M 5200 (polyurethane) may not even do it. Boatlife polysulfide might work.

I have a pair of cheap Shimano touring shoes that the soft pliable sole had debonded from the rest, nothing I have found works so far, kind of bummed, they were closeout and did the job for short jaunts to the coffee house. On those the sole is who knows what, it is not silicone, but presents a waxy feel. Unglutanium.