Add lessons Phase 2: schedule slots with conflict detection

Recurring weekly time slots linking instructors to lesson types.
Includes day/time overlap detection, instructor and day-of-week
filtering, and 17 new integration tests (40 total lessons tests).

packages/backend/src/db/migrations/0029_schedule_slots.sql

@@ -0,0 +1,14 @@
+-- Phase 2: Schedule slots — recurring weekly time slots
+
+CREATE TABLE "schedule_slot" (
+  "id" uuid PRIMARY KEY DEFAULT gen_random_uuid(),
+  "instructor_id" uuid NOT NULL REFERENCES "instructor"("id"),
+  "lesson_type_id" uuid NOT NULL REFERENCES "lesson_type"("id"),
+  "day_of_week" integer NOT NULL,
+  "start_time" time NOT NULL,
+  "room" varchar(100),
+  "max_students" integer NOT NULL DEFAULT 1,
+  "is_active" boolean NOT NULL DEFAULT true,
+  "created_at" timestamptz NOT NULL DEFAULT now(),
+  "updated_at" timestamptz NOT NULL DEFAULT now()
+);

packages/backend/src/db/migrations/meta/_journal.json

@@ -204,6 +204,13 @@
       "when": 1774880000000,
       "tag": "0028_lessons_foundation",
       "breakpoints": true
+    },
+    {
+      "idx": 29,
+      "version": "7",
+      "when": 1774890000000,
+      "tag": "0029_schedule_slots",
+      "breakpoints": true
     }
   ]
 }