How to add `last-updated` to the LLM prompt?

Configuration Voice Assistant
1

When using conversation.process, I can ask about the state of exposed entities. I’d like to tweak this to add the last-updated value of the sensors as well.

  1. How is the prompt to the LLM constructed? (I have both Gemini and ChatGPT configured.)
  2. How can I debug what is being sent to the LLM via the API?

(For #2, I’ve tried setting homeassistant.components.conversation: debug, but don’t see anything in the logs.)

Any pointers in the code or docs on how to modify the template?