Linux user is in group but does not have group permissions

386699 4 drw-rw----  2 root docker 4096 Nov 17 20:03 vault

No x in rw-rw---- for vault indicates the directory is not executable for anyone. The root user is not denied access though, regular users are.

You need the x bit to access files inside the directory. See:

• Execute vs Read bit. How do directory permissions in Linux work?
• Do I really need recursive chmod to restrict access to a folder?

chmod g+x vault is what you need. The resulting permissions will be rw-rwx---. It's somewhat unusual to have x for the owning group and not for the owning user; but since the owner is root, it won't matter much in this case.

In general (i.e. when the owner is not necessarily root) rwxrwx--- makes more sense than rw-rwx---, unless the owner has a reason to restrict access for himself. Note the owning user's permissions matter for the owner even if he's in the owning group.