✨(backend) introduce a configurable analytics system

Add an analytics abstraction that allows configuring which analytics
solution the app uses. PostHog is implemented as one backend, but by
default no analytics backend is activated.

The goal is to track events in a sufficiently organized way and to
let any developer implement their own backend as long as it follows
the same protocol.

src/backend/core/analytics/base.py

@@ -0,0 +1,50 @@
+"""Analytics backend protocol and default no-op implementation."""
+
+from typing import Any, Protocol
+
+from ..models import User
+from .events import AnalyticsEvent
+
+
+class AnalyticsBackend(Protocol):
+    """
+    Interface every analytics backend must implement.
+
+    Backends are instantiated once (singleton) with the kwargs declared in
+    settings.ANALYTICS_BACKEND_SETTINGS, e.g.:
+
+        ANALYTICS_BACKEND = "core.analytics.posthog.PostHogAnalytics"
+        ANALYTICS_BACKEND_SETTINGS = {"api_key": "...", "host": "..."}
+    """
+
+    def __init__(self, **kwargs: Any) -> None: ...
+
+    def identify(self, user: User, properties: dict[str, Any] | None = None) -> None:
+        """Associate traits (email, name, ...) with an identified user."""
+
+    def capture(
+        self,
+        user: User,
+        event: AnalyticsEvent,
+        properties: dict[str, Any] | None = None,
+    ) -> None:
+        """Record an event performed by an identified user."""
+
+    def shutdown(self) -> None:
+        """Flush pending events. Called on process exit."""
+
+
+class NoOpAnalytics:
+    """Default backend: silently discards everything."""
+
+    def __init__(self, **kwargs: Any) -> None:
+        """No-op: accepts and ignores any backend settings kwargs."""
+
+    def identify(self, user: User, properties=None) -> None:
+        """No-op: discards identify calls."""
+
+    def capture(self, user, event, properties=None) -> None:
+        """No-op: discards captured events."""
+
+    def shutdown(self) -> None:
+        """No-op: nothing to flush."""