Why did the agent not send anything?

Almost always because approving a draft is not the same as sending it. Approving puts the message in the queue. Approved messages then leave during business hours at a steady pace, so a batch you approve late in the evening will not move until the next working morning. The pacing is deliberate, and nothing is broken.

The other reasons

• Nothing is approved yet. Every message is a draft until you approve it, and nothing sends on its own.
• No account is connected. Finding and qualifying people needs nothing connected, but invites and messages act through your own account.
• You are not connected to them yet. A bare connection invite goes first, and the message to approve appears only after they accept.
• Your session expired. Account actions pause on their own until you reconnect, and your chats and drafts are kept.
• You reached a daily limit. Only that action pauses, and a live chat resumes the next day.
• They already have an open thread. Each person gets one outreach thread, so the same person surfacing in another chat gets no second first touch.
• They replied first. A reply cancels any scheduled message automatically.