Currently I can get the doorbell alert to my Nest Audio Speaker... never even had to set anything up just did it from day 1. Recently I installed the Nest Mesh Wifi where the two extra access points are also speakers / google assistant. I've been through all of the settings, turned on the personalized notifications... but those access point speakers do not chime or say "someone is at the front door doorbell" when someone rings the Nest doorbell... seems kind of silly that this wouldn't be possible but here I am...
When "Visitor announcements" is turned on for a Google Nest doorbell, it broadcasts doorbell announcements to all speakers or displays in the same Google Nest "home". Perhaps when you add new speakers, there's a delay before they get propagated on Google Nest's servers.
@MplsCustomer, thanks for the help.
@embracemaking, thanks for posting and for being a step ahead of us. Try to turn off the do not disturb and see if this will make any difference. Check the steps below.