fix: resolve customer unread indicators

[mafirs]

Summary

Fix customer unread indicators that could remain stuck when the latest chat message is not visible to customers.

Root Cause

Customer ticket detail only loads non-internal messages, but the customer ticket list and read/unread filtering used the latest message across all chat messages. If the latest message was internal, customers could not see or mark that message as read, so the sidebar unread dot could reappear after switching tickets.

Changes

• Filter customer ticket-list latest-message lookup to customer-visible messages.
• Apply the same customer-visible filtering to read/unread ticket filtering.
• Make read-status sending wait for an open WebSocket connection.
• Only clear local unread state after read-status sending succeeds.

Verification

• Ran bun run typecheck
• Ran git diff --check upstream/main..origin/fix/user-unread
• Confirmed PR branch comparison against labring/tentix:main is ahead by 1 commit with 4 changed files.

Notes

Please merge with Create a merge commit.

[github-actions]

🤖 Fork Repository Check Complete

✅ Basic security scan completed
✅ Dependency check completed
✅ Linting check completed
✅ Build test completed

This PR from a fork repository has passed basic safety checks. A maintainer will review the changes before running full CI/CD pipeline.

This is an automated safety check for contributions from fork repositories.