Muting Agent Microphone via Genesys Cloud JavaScript Client SDK

Is it possible to programmatically mute or unmute an agent’s microphone during an active call using the Genesys Cloud JavaScript Client SDK?

I am building a Salesforce integration that requires automated audio control based on Data Action triggers. I have initialized the ConversationCallApi and can retrieve the conversation ID, but I cannot find a method to toggle the local audio stream.

“The Client SDK provides methods for joining and leaving conversations, but specific media controls may require WebSocket signaling.”

I attempted calling updateConversationParticipant with muted: true, but the API returned 400 Bad Request. Here is my current payload:

{
 "muted": true
}

How do I correctly invoke the mute command?