Describe the bug
When sending messages from the TUI (terminal UI), the session's origin.channel is recorded as "webchat" instead of "tui". This causes assistant replies to be delivered to the webchat client instead of back to the TUI in real-time.

To Reproduce

1. Connect to Gateway via openclaw tui
2. Send a message
3. Observe: reply appears in webchat (macOS menu bar app), not in TUI
4. Restart TUI → old messages appear in history, but real-time delivery still fails

Expected behavior
Replies should be delivered back to TUI in real-time, not to webchat.

Session origin (from sessions.json):

"origin": {
  "provider": "webchat",
  "surface": "webchat",
  "chatType": "direct",
  "label": "openclaw-tui"
},
"lastChannel": "webchat"

Environment

• macOS
• OpenClaw latest
• TUI mode

Additional context
The TUI client should have its own channel identity (e.g., "tui") rather than being mapped to "webchat". The channel list in docs only includes: whatsapp, telegram, discord, slack, signal, imessage, webchat — TUI is missing.