Hey Everyone,
I found the problem with why the Intercom wasn't working. It was due to some false assumptions on my side. For some reason, I thought when I would make an announcement from one of my iOS devices, the announcement would go to all my devices including the Homepod. However, that is not the case. It only goes to iOS devices that have a different Home account. In the case of my wife, I sent an invite and added her phone to the announcement. When the announcement goes out, she then gets an announcement.
And when going through Homepod, I couldn't initially send announcements as it was just my devices and Homepod knows who I am. So by design, it wouldn't go to devices. Now that my wife is added, it works well. I can understand that design is efficient and I can accept it. If I want to use a tablet for handling announcements, I could just use a free icloud account on that separate tablet. However, since I'm really liking Homepod, I'm more inclined to go with that.