Directly mount btrfs subvolume or bind mount if already visible

Problem #1 was caused by SELinux. Since I don't need it for this system, I simply disabled it.

Problem #2 was caused by a udev setting (specified in systemd script) that makes the udev namespace keep a 'slave' copy of the mount flags. Changing this to 'shared' fixed the problem. See a more detailed answer here: https://unix.stackexchange.com/a/154318/41988

btrfs subvolume show /directory/in/question

Most likely you need sudo. The command will succeed if it's a subvolume; it will fail otherwise. You can redirect output to /dev/null and rely solely on the exit status.

This will test every directory available in the directory tree:

sudo find / -type d -exec sh -c '
   for d do
      btrfs subvolume show "$d" >/dev/null 2>&1 && printf "%s\n" "$d"
   done' find-sh {} +

You may want to exclude paths that are beyond suspicion. The following code excludes /proc, /sys and /dev:

sudo find / -type d \( \
     \( -path /proc -prune \) -o \
     \( -path /sys -prune \) -o \
     \( -path /dev -prune \) -o \
     \( -exec sh -c '
        for d do
           btrfs subvolume show "$d" >/dev/null 2>&1 && printf "%s\n" "$d"
        done
     ' find-sh {} + \) \)

Related: How to determine which subvolume a directory/file is on?