Cannot access /proc/<pid>/exe of shared proc filesystem

[agorgl]

What causes the following behavior?

$ bwrap --dev-bind / / bash -c "ls /proc/$$/exe"
ls: cannot access '/proc/396260/exe': Permission denied

I have program that checks /proc/$ppid/exe to check if its' parent process is alive, and this fails, similar to the POC above when sandboxed. Why is that?