(refactor) Normalize runtime config labels

Hide the old pobsync_home field from the Django admin and replace legacy
operator-facing labels with runtime state root and backup root terminology.

Rename admin compatibility fieldsets, update self-check/config-check text,
and refresh management command help so Django/systemd stays the primary
mental model.

src/pobsync_backend/tests/test_admin.py

@@ -5,11 +5,25 @@ from datetime import datetime, timezone
 from django.contrib.admin.sites import AdminSite
 from django.test import TestCase
 
-from pobsync_backend.admin import BackupRunAdmin, HostConfigAdmin, SnapshotRecordAdmin
-from pobsync_backend.models import BackupRun, HostConfig, ScheduleConfig, SnapshotRecord
+from pobsync_backend.admin import BackupRunAdmin, GlobalConfigAdmin, HostConfigAdmin, SnapshotRecordAdmin
+from pobsync_backend.models import BackupRun, GlobalConfig, HostConfig, ScheduleConfig, SnapshotRecord
 
 
 class AdminDisplayTests(TestCase):
+    def test_admin_hides_old_global_state_field_and_uses_compatibility_label(self) -> None:
+        site = AdminSite()
+        global_admin = GlobalConfigAdmin(GlobalConfig, site)
+        host_admin = HostConfigAdmin(HostConfig, site)
+
+        global_fieldsets = list(global_admin.fieldsets)
+        host_fieldsets = list(host_admin.fieldsets)
+        global_fields = [field for _name, options in global_fieldsets for field in options["fields"]]
+        fieldset_names = [name for name, _options in [*global_fieldsets, *host_fieldsets]]
+
+        self.assertNotIn("pobsync_home", global_fields)
+        self.assertIn("Compatibility data", fieldset_names)
+        self.assertNotIn("Legacy JSON", fieldset_names)
+
     def test_host_admin_links_to_related_snapshots_and_runs(self) -> None:
         site = AdminSite()
         admin = HostConfigAdmin(HostConfig, site)