I use Conversation Essentials or a similar add-on for conversation enhancements. Some of their features for conversation messages do not appear as expected. What can I do?

Check their template modifications for any modifications to the "message" or "conversation_message" templates. If there are any of them, create additional template modifications applying the same changes to the "wmt_lcc_message" and "wmt_lcc_conversation_message" templates accordingly.