chromium looks for the messaging extension (used to communicate with gnome-shell) in /etc/chromium/native-messaging-hosts/, which appears to be allowed by the apparmor profile:
$ grep -n “/etc/chromium” /var/lib/snapd/apparmor/profiles/snap.chromium.chromium 1250:/etc/chromium/{,**} r,
stracing the snap reveals that /usr/bin/chrome-gnome-shell cannot be found in the context of the snap:
15760 access(“/usr/bin/chrome-gnome-shell”, F_OK) = -1 ENOENT (No such file or directory)
This is not an apparmor denial. Inside the snap’s execution environment, /usr/bin is in fact /snap/core/current/usr/bin.