Add OpenAPI docs, frontend, migrations, and API updates

- OpenAPI: add missing endpoints (add-from-url, subscriptions, public availability)
- OpenAPI: CalendarSubscription schema, Subscriptions tag
- Frontend app
- Migrations: count_for_availability, subscriptions_sync, user_preferences, calendar_settings
- Config, rate limit, auth, calendar, booking, ICS, availability, user service updates

Made-with: Cursor

internal/api/openapi/specs/schemas.json

@@ -58,7 +58,7 @@
           "name": { "type": "string", "minLength": 1, "maxLength": 80 },
           "color": { "type": "string", "pattern": "^#[0-9A-Fa-f]{6}$", "example": "#22C55E" },
           "is_public": { "type": "boolean" },
-          "ical_url": { "type": "string", "format": "uri", "description": "Public iCal feed URL (only present when is_public is true)" },
+          "ical_url": { "type": "string", "format": "uri", "description": "iCal feed URL. Present for both public and private calendars. Public calendars use a shorter token; private calendars use a 64-character SHA256 hex token for additional security." },
           "role": { "type": "string", "enum": ["owner", "editor", "viewer"], "description": "Current user's role on this calendar" },
           "created_at": { "type": "string", "format": "date-time" },
           "updated_at": { "type": "string", "format": "date-time" }
@@ -152,6 +152,18 @@
           "role": { "type": "string", "enum": ["owner", "editor", "viewer"] }
         }
       },
+      "CalendarSubscription": {
+        "type": "object",
+        "required": ["id", "calendar_id", "source_url", "created_at"],
+        "properties": {
+          "id": { "type": "string", "format": "uuid" },
+          "calendar_id": { "type": "string", "format": "uuid" },
+          "source_url": { "type": "string", "format": "uri", "description": "iCal feed URL" },
+          "last_synced_at": { "type": "string", "format": "date-time", "nullable": true },
+          "sync_interval_minutes": { "type": "integer", "nullable": true },
+          "created_at": { "type": "string", "format": "date-time" }
+        }
+      },
       "BusyBlock": {
         "type": "object",
         "required": ["start", "end", "event_id"],