fix(question-types): realign registry ids with the question_type table

The registry hardcoded numeric ids that drifted from the database
`question_type` table: MATCHING and HOTSPOT were inserted mid-list
(ids 9 and 11) but never seeded, shifting ORDERING/LINK/WORD_BANK/
STAR/VIDEO_RECORDING one or two ids past their real rows. Every id
emitter inherited the wrong values — the exercise editor, the AI
question generator, and the grading/scoring gate — so e.g. an ORDERING
question was stored as id 10 (LINK in the DB), came back as a manual
type, and never auto-graded.

- Move MATCHING/HOTSPOT to the end (ids 14/15) and flag them
  `disabled`, restoring the append-only id convention and realigning
  ORDERING=9, LINK=10, WORD_BANK=11, STAR=12, VIDEO_RECORDING=13 with
  the DB.
- Add a registry test asserting every enabled type's id matches the
  canonical `question_type` rows and disabled types stay past the live
  range, so ids can't silently drift again.
- Constrain the agent tool schema to enabled, DB-backed ids so the
  model can't emit a disabled id with no row.
- Drop disabled types from the teacher prompt's type list and guidance.
- Centralize the dashboard question-type picker on the `disabled` flag.

This also fixes video-recording detection, which compared against the
stale id 15 instead of the real 13.

packages/core/src/services/agent/agent-tool-schemas.ts

@@ -5,11 +5,22 @@ import {
   LANDING_PAGE_METADATA_DESCRIPTION_SECTION_HINT,
   LANDING_PAGE_SECTION_HTML_AGENT_HINT
 } from '@cio/ai-assistant/tools';
-import { QUESTION_TYPE_REGISTRY } from '@cio/question-types';
+import { ENABLED_QUESTION_TYPE_REGISTRY } from '@cio/question-types';
 import { ZExerciseSectionAfterBehavior } from '@cio/utils/validation/exercise';
 import { ZCourseLandingPageUpdate, ZCourseLandingPageMetadataUpdateFields } from '@cio/utils/validation/course';
 
 // courseId is NOT a parameter — it's injected from the authenticated request context.
+
+// Only question types backed by a `question_type` DB row may be generated.
+// Disabled types (e.g. MATCHING/HOTSPOT) have no row and would fail the FK, so
+// the model is constrained to the enabled ids rather than the whole registry.
+const ENABLED_QUESTION_TYPE_IDS = ENABLED_QUESTION_TYPE_REGISTRY.map((type) => type.id);
+const zEnabledQuestionTypeId = z
+  .number()
+  .int()
+  .refine((id) => ENABLED_QUESTION_TYPE_IDS.includes(id), {
+    message: `questionTypeId must be one of: ${ENABLED_QUESTION_TYPE_IDS.join(', ')}`
+  });
 // This prevents prompt injection from tricking the LLM into targeting another course.
 
 export const emptyParam = z.object({});
@@ -63,14 +74,9 @@ export const updateContentParam = z.object({
 
 export const questionSchema = z.object({
   question: z.string().min(1),
-  questionTypeId: z
-    .number()
-    .int()
-    .min(1)
-    .max(QUESTION_TYPE_REGISTRY.length)
-    .describe(
-      'Required. Use the numeric question type IDs from the teacher system prompt (Question Types). Omitting this field is invalid — set an explicit type on every question and vary types within each exercise.'
-    ),
+  questionTypeId: zEnabledQuestionTypeId.describe(
+    'Required. Use the numeric question type IDs from the teacher system prompt (Question Types). Omitting this field is invalid — set an explicit type on every question and vary types within each exercise.'
+  ),
   points: z.number().min(0).default(1),
   order: z.number().int().min(0),
   options: z.array(z.object({ label: z.string().min(1), isCorrect: z.boolean() }))
@@ -193,7 +199,7 @@ export const updateQuestionPatchSchema = z
   .object({
     id: z.number().int(),
     question: z.string().min(1).optional(),
-    questionTypeId: z.number().int().min(1).max(QUESTION_TYPE_REGISTRY.length).optional(),
+    questionTypeId: zEnabledQuestionTypeId.optional(),
     points: z.number().min(0).optional(),
     order: z.number().int().min(0).optional(),
     exerciseSectionId: z