fix: prevent failed containers from showing as running on dashboard

- Add final get_container_status check in start_tool_instance before
  writing status=running; mark as error and return logs if container stopped
- Treat restarting as error in HealthMonitor when DB status was already
  running, so crash loops are surfaced instead of preserved
- Disable auto-restart (restart: unless-stopped -> restart: no) for tool
  instances in manifest compiler, legacy dockerfile path, and built-in seeds

Quality gates:
- pytest tests/unit: 210 passed
- ruff: clean on changed files
- mypy: clean on changed files

openspec/changes/fix-container-status-false-positive/.pi-map.md

@@ -0,0 +1,20 @@
+# openspec/changes/fix-container-status-false-positive
+dir: openspec/changes/fix-container-status-false-positive
+
+index: openspec/changes/fix-container-status-false-positive/.pi-map.index.md
+
+## role
+Documents a bug fix for correcting container status false positives where failed containers incorrectly appeared as running in a dashboard/monitoring system.
+## files
+- change.md | Documents a bug fix for failed containers incorrectly displaying as running on a dashboard, detailing root cause analysis and the fix implementation across multiple files.
+- tasks.md | Track progress of fixing a false-positive running status bug in a container/system management system
+## arch
+Issue-tracking documentation pattern using markdown files (change.md for technical specification, tasks.md for progress tracking) to manage a bug fix across multiple system components.
+## tags
+bug, fix, running, change, system, tasks, documents, failed
+## symbols
+-
+## workflows
+-
+## dirty
+-