[BUG] send_message can over-confirm sends and miss share-info prompt

[ghul0]

Setup

• Repository branch: local development against upstream/main
• Tool: send_message
• Runtime/client: MCP clients using the browser-backed LinkedIn session

What Happened

send_message can report sent: true by finding the outgoing message text anywhere on the page, including text that is still present in the editable composer or was already present in the visible conversation UI before the send attempt completed.

Some LinkedIn message sends can also show a post-Send prompt asking whether to share profile/contact information with the recipient. The current flow has no explicit handling for that prompt, so it can leave the send unconfirmed or make the final state ambiguous. The safer default after the operator has approved only the message body is to avoid sharing additional profile/contact information.

Steps to Reproduce

1. Open a message compose flow via send_message with confirm_send=true.
2. Use message text that is already visible in the page or remains in the composer while LinkedIn is still processing the send.
3. Trigger a LinkedIn post-Send prompt asking whether to share profile/contact information, where available.
4. Observe that the tool can treat page text presence as confirmation instead of requiring a new non-composer occurrence after the send attempt, and it does not explicitly choose the no-share path for the profile/contact-info prompt.

Logs

No logs with private LinkedIn content are attached. The issue is based on the existing send_message confirmation path and reproduced with unit-level tests to avoid sending additional live LinkedIn messages during development.