I discovered today that the mechanism for transferring callers from a queue to a voicemail when agents are unable to answer the call today is... well, a little less than elegant. Once a call is inside of a queue, it can only be transferred to a 'Person in organization' (individual mailbox) or a Voice App:
This limitation exists for both the maximum number of calls and for call time out. This means that if you are wanting to redirect calls that are not answered agents in the middle of typical operating hours, it is necessary to create another auto attendant that has default behavior of submitting voicemail to a group. To create another auto attendant, it is necessary to create a new resource account; ensure that you use your @*mytenantname*.onmicrosoft.com domain when creating resource accounts:
After naming the auto attendant (I suggest using a name that is similar but not identical to the resource account), in the call flow you can select 'No greeting' and 'Redirect call' to an existing group voicemail destination. I did not know that regular Office 365/Teams groups are automatically voicemail-enabled until I had done a substantial amount of digging. I do believe, however, that in order to access the shared voicemail that is sent to the group that members have to have a Teams Phone System license.
The next options about call flow for after hours/holidays should be fairly straightforward/default because we are only creating this AA for the purpose of redirecting callers to voicemail. Make sure to assign the resource account that we just created:
Now, let's return to our queue and assign the overflow/timeout settings to our resource account created for this purpose:
Obviously, the folks working on the old Skype for Business/Teams PSTN stuff should have a more slick implementation for this, but setting up another auto attendant - while clunky - achieves the desired effect.