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/.pi-map.index.md

@@ -2,7 +2,7 @@
 dir: openspec/changes
 
 ## role
-Manages and tracks specification changes, diffs, and versioning history for OpenAPI documents.
+Provides change-tracking and diffing utilities for OpenAPI specification evolution and version comparison.
 ## parent
 index: openspec/.pi-map.index.md
 map: openspec/.pi-map.md
@@ -10,6 +10,9 @@ map: openspec/.pi-map.md
 - openspec/changes/archive
   index: openspec/changes/archive/.pi-map.index.md
   map: openspec/changes/archive/.pi-map.md
+- openspec/changes/fix-container-status-false-positive
+  index: openspec/changes/fix-container-status-false-positive/.pi-map.index.md
+  map: openspec/changes/fix-container-status-false-positive/.pi-map.md
 - openspec/changes/fix-pi-container-mount-permissions
   index: openspec/changes/fix-pi-container-mount-permissions/.pi-map.index.md
   map: openspec/changes/fix-pi-container-mount-permissions/.pi-map.md