Unfortunately, Apple ruined this feature too in Catalina. Dictation was removed from Accessibility and with it was gone the "Mute audio output while dictating" option, that could be enabled or disabled.
You could try this, but I'm not sure it will work
- disable Dictation from Keyboard
- enable Voice Control from Accessibility, wait if it wants to download language files, disable it
- run this command in Terminal
defaults write com.apple.speech.recognition.AppleSpeechRecognition.prefs DictationIMAllowAudioDucking -bool NO