My hunch is Apple considers these workout reminders as time sensitive. Have you reviewed your announcement settings? You could should be able to turn all of them off or just for that app. 

> Siri automatically enables app notifications for apps that use time-sensitive notifications, but you can change the settings at any time. 

> Go to Settings  > Siri & Search > Announce Notifications, then turn on Announce Notifications.

In your case, if you want Siri to not announce notifications from the workout app, then turn off Announce Notifications for that app.

- https://support.apple.com/guide/iphone/have-siri-announce-calls-and-notifications-iph838fd6fd4/ios

If the above setting doesn’t work, you’ll have to choose to disable detection (which you don’t want either)

> To turn this setting on or off, open the Settings app on your Apple Watch, tap Workout, then go to Start Workout Reminder or End Workout Reminder.

From the [Workout app manual][1]. 


  [1]: https://support.apple.com/en-us/101171#forgetto