It is not the right class to use to deserialize.
"GET/api/v2/conversations" returns a ConversationEntityListing (with Conversation in it). In the Conversation class, the participants are instances of the "Participant" class.
The CallMediaParticipant class is related to another endpoint - "GET/api/v2/conversations/calls".
This endpoint returns a CallConversationEntityListing (with CallConversation in it). In the CallConversation class, the participants are instances of the "CallMediaParticipant" class.
You are right, thank you for the precision ! I was mixing both calls (GET/api/v2/conversations vs GET/api/v2/conversations/calls.)
Thanks again for your help.