T-05: Remove app.state mutation from _build_app_context

Move session cache initialization from per-request _build_app_context to
startup lifespan handler. The session cache type is now decided once at app
startup based on settings, making _build_app_context pure (read-only).

Changes:
- Move cache initialization logic to new _update_session_cache() in main.py
- Call _update_session_cache() during lifespan startup to initialize cache
- Remove three if/elif/elif branches mutating state.session_cache from _build_app_context
- Add cache swap logic to set_runtime_settings() in runtime_state.py to handle
  runtime settings changes (e.g., setup wizard updates)
- Keep app.state.session_cache initialization in create_app() for test compatibility

This ensures:
- _build_app_context is pure and doesn't mutate app state on each request
- Session cache configuration decisions are centralized at startup
- Settings changes during runtime (via setup wizard) also trigger cache swap
- Cache initialization logic is isolated in one place

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

backend/app/utils/runtime_state.py

@@ -24,6 +24,7 @@ from starlette.datastructures import State
 
 from app.models.config import PendingRecovery
 from app.models.server import ServerStatus
+from app.utils.session_cache import InMemorySessionCache, NoOpSessionCache
 
 if TYPE_CHECKING:  # pragma: no cover
     from app.config import Settings
@@ -118,10 +119,25 @@ def get_effective_settings(app: Any) -> Settings:
 
 
 def set_runtime_settings(app: Any, settings: Settings) -> None:
-    """Store the resolved runtime settings separately from bootstrap config."""
+    """Store the resolved runtime settings separately from bootstrap config.
+
+    Also updates the session cache backend if the session cache configuration
+    has changed, replacing it with InMemorySessionCache or NoOpSessionCache
+    as appropriate.
+
+    Args:
+        app: The FastAPI application instance.
+        settings: The new effective settings.
+    """
     runtime_state = get_runtime_state(app)
     runtime_state.runtime_settings = settings
 
+    # Update session cache if settings changed
+    cache_enabled = settings.session_cache_enabled and settings.session_cache_ttl_seconds > 0.0
+    new_cache = InMemorySessionCache() if cache_enabled else NoOpSessionCache()
+    app.state.session_cache = new_cache
+    log.debug("session_cache_updated", cache_type=type(new_cache).__name__)
+
 
 def update_app_settings(app: Any, **overrides: Any) -> None:
     """Update the current effective settings immutably."""