You should be able to turn on both the "Indoor chime" option and the "Visitor announcements" option at the same time.
The only thing that should prevent this is if your battery doorbell is NOT wired. In that case, it is not connected to your indoor doorbell chime and your doorbell transformer, so it is impossible to ring that indoor doorbell chime and the "Indoor chime" is therefore grayed out in the Google Home app.
By the way, if this is actually your question, when you turn on "Visitor announcements" (https://support.google.com/googlenest/answer/7672451), you get BOTH a verbal announcement ("Someone's at the front door") AND a chime sound; there is no way to get just one or the other.
@MCC, thanks for reaching out here in the Community. How's it going with your Nest Camera? Were you able to read what MplsCustomer has shared? In case you have an update you know where to find us.
I appreciate the help, MplsCustomer.