Update observability docs and task utilities

- Add Observability.md documentation
- Standardize task logging with correlation_id support
- Add log_sanitizer utility for PII masking
- Update Tasks.md tracking
- Update geo_cache tasks and other task modules with correlation_id

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/app/tasks/health_check.py

@@ -13,11 +13,15 @@ keys).  If the health probe subsequently detects an online→offline transition
 within 60 seconds of that activation, a
 :class:`~app.models.config.PendingRecovery` record is written to
 ``app.state.pending_recovery`` so the UI can offer a one-click rollback.
+
+Correlation IDs are propagated through the task using :mod:`app.utils.correlation`
+so that task logs can be correlated across runs.
 """
 
 from __future__ import annotations
 
 import datetime
+import uuid
 from typing import TYPE_CHECKING
 
 import structlog
@@ -25,6 +29,7 @@ import structlog
 from app.models.server import ServerStatus
 from app.services import health_service
 from app.tasks.timeout_utils import run_with_timeout
+from app.utils.correlation import reset_correlation_id, set_correlation_id
 from app.utils.runtime_state import (
     RuntimeState,
     get_effective_settings,
@@ -47,13 +52,30 @@ HEALTH_CHECK_INTERVAL: int = 30
 HEALTH_PROBE_TIMEOUT_SECONDS: int = 10
 
 
-async def _run_probe_with_resources(settings: Settings, runtime_state: RuntimeState) -> None:
+async def _run_probe_with_resources(
+    settings: Settings,
+    runtime_state: RuntimeState,
+    correlation_id: str | None = None,
+) -> None:
     """Probe fail2ban and cache the result on the runtime state.
 
     Args:
         settings: The resolved application settings used for the probe.
         runtime_state: The mutable runtime state manager.
+        correlation_id: Optional correlation ID for log correlation.
     """
+    if correlation_id is None:
+        correlation_id = str(uuid.uuid4())
+
+    token = set_correlation_id(correlation_id)
+    try:
+        await _do_probe_with_resources(settings, runtime_state)
+    finally:
+        reset_correlation_id(token)
+
+
+async def _do_probe_with_resources(settings: Settings, runtime_state: RuntimeState) -> None:
+    """Inner probe logic that runs with correlation context set."""
 
     async def _do_probe() -> None:
         socket_path: str = settings.fail2ban_socket