I set up Rhasspy and configured it to use HomeAssistant for intent handling. I see the intent is handled by HomeAssistant, but Rhasspy does not answer my question.
The intent_script you have created is using the TTS from HA (this is what the speech part does)
It is not sending a text to Rhasspy, that is why you do not hear Rhasspy speech.
Check here if you want Rhasspy to process the text: