automatic reply from distribution group using shared mailbox

The business asked me to configure an auto-reply from a distribution group (which I understand is not a thing). After some research, I created a new shared mailbox, configured an automatic reply (OOO) on the mailbox, then added the mailbox to the distribution group, with the expectation that any message sent to the group would elicit an automatic reply from the shared mailbox (one reply per sender, as any OOO configuration would do).

The automatic reply works when a message is sent directly to the shared mailbox, but no automatic reply is generated when a message is sent to the group.

Did I miss something or is this configuration not supported? I've considered using an inbox rule using the have server reply with message option, but that can cause looping and I prefer the one reply per sender solution that the OOO mechanism provides. Any advice is welcome. Thanks!