Hello Lanmc54,
You do need to have headphones, or use CarPlay, to have Siri announce calls and notifications. Be sure that you have the following settings enabled:
"Siri can announce calls and notifications from apps like Messages on supported headphones and when using CarPlay. You can answer or reply using your voice without needing to say “Hey Siri.”
Announce Calls and Announce Notifications also work with supported third-party apps.
Have Siri announce calls
With Announce Calls, Siri identifies incoming phone calls and FaceTime calls, which you can accept or decline using your voice.
- Go to Settings
> Siri & Search > Announce Calls, then choose an option. - When a call comes in, Siri identifies the caller, and asks if you want to answer the call. Say “yes” to accept the call or “no” to decline it."
More details here: Announce calls, messages, and more with Siri on iPhone
If the feature is not working as expected, be sure to secure your data with a backup and complete the latest software update: Update your iPhone or iPad
We hope this helps.
Take care.