What does this PR do?

Background process watch notifications can lose the Discord thread context when the stored session origin does not carry the current event thread. This PR uses the event thread information as a fallback so watch notifications return to the thread where the process was started.

Related Issue

Fixes #10411

Type of Change

• 🐛 Bug fix (non-breaking change that fixes an issue)
• ✨ New feature (non-breaking change that adds functionality)
• 🔒 Security fix
• 📝 Documentation update
• ✅ Tests (adding or improving test coverage)
• ♻️ Refactor (no behavior change)
• 🎯 New skill (bundled or hub)

Changes Made

• Preserve Discord thread routing for watch/process notifications in gateway/run.py.
• Add focused regression coverage for event-thread fallback routing.

How to Test

1. Check out this PR branch.
2. Run: .venv/bin/python -m pytest -o 'addopts=' tests/gateway/test_watch_notification_thread_routing.py -q
3. Expected result: 6 passed

Checklist

Code

• I've read the Contributing Guide
• My commit messages follow Conventional Commits (fix(scope):, feat(scope):, etc.)
• I searched for existing PRs to make sure this isn't a duplicate
• My PR contains only changes related to this fix/feature (no unrelated commits)
• I've run pytest tests/ -q and all tests pass — focused pytest passed; full suite was not run in this salvage pass
• I've added tests for my changes (required for bug fixes, strongly encouraged for features)
• I've tested on my platform: Linux container / Python 3.11

Documentation & Housekeeping

• I've updated relevant documentation (README, docs/, docstrings) — or N/A
• I've updated cli-config.yaml.example if I added/changed config keys — or N/A
• I've updated CONTRIBUTING.md or AGENTS.md if I changed architecture or workflows — or N/A
• I've considered cross-platform impact (Windows, macOS) per the compatibility guide — or N/A
• I've updated tool descriptions/schemas if I changed tool behavior — or N/A

Screenshots / Logs

Focused verification:

`.venv/bin/python -m pytest -o 'addopts=' tests/gateway/test_watch_notification_thread_routing.py -q` — 6 passed