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/question-types/src/question-type-registry.ts

@@ -74,29 +74,11 @@ export const QUESTION_TYPE_REGISTRY: readonly QuestionTypeMetadata[] = [
     supportsPartialCredit: false,
     manualGradingRequired: true
   },
-  {
-    key: QUESTION_TYPE_KEY.MATCHING,
-    typename: 'MATCHING',
-    label: 'Matching',
-    id: 9,
-    autoGradable: true,
-    supportsPartialCredit: true,
-    manualGradingRequired: false
-  },
   {
     key: QUESTION_TYPE_KEY.ORDERING,
     typename: 'ORDERING',
     label: 'Ordering',
-    id: 10,
-    autoGradable: true,
-    supportsPartialCredit: true,
-    manualGradingRequired: false
-  },
-  {
-    key: QUESTION_TYPE_KEY.HOTSPOT,
-    typename: 'HOTSPOT',
-    label: 'Hotspot',
-    id: 11,
+    id: 9,
     autoGradable: true,
     supportsPartialCredit: true,
     manualGradingRequired: false
@@ -105,7 +87,7 @@ export const QUESTION_TYPE_REGISTRY: readonly QuestionTypeMetadata[] = [
     key: QUESTION_TYPE_KEY.LINK,
     typename: 'LINK',
     label: 'Links',
-    id: 12,
+    id: 10,
     autoGradable: false,
     supportsPartialCredit: false,
     manualGradingRequired: true
@@ -114,7 +96,7 @@ export const QUESTION_TYPE_REGISTRY: readonly QuestionTypeMetadata[] = [
     key: QUESTION_TYPE_KEY.WORD_BANK,
     typename: 'WORD_BANK',
     label: 'Word bank',
-    id: 13,
+    id: 11,
     autoGradable: true,
     supportsPartialCredit: true,
     manualGradingRequired: false
@@ -123,7 +105,7 @@ export const QUESTION_TYPE_REGISTRY: readonly QuestionTypeMetadata[] = [
     key: QUESTION_TYPE_KEY.STAR,
     typename: 'STAR',
     label: 'Star rating',
-    id: 14,
+    id: 12,
     autoGradable: true,
     supportsPartialCredit: false,
     manualGradingRequired: false
@@ -132,13 +114,40 @@ export const QUESTION_TYPE_REGISTRY: readonly QuestionTypeMetadata[] = [
     key: QUESTION_TYPE_KEY.VIDEO_RECORDING,
     typename: 'VIDEO_RECORDING',
     label: 'Video recording',
-    id: 15,
+    id: 13,
     autoGradable: false,
     supportsPartialCredit: false,
     manualGradingRequired: true
+  },
+  // Built but not offered in the product. Kept at the END of the id sequence
+  // (append-only) so they never shift the ids of types that exist in the DB.
+  // They have no `question_type` row, so `disabled` keeps them out of pickers,
+  // the AI tool enum, and validation.
+  {
+    key: QUESTION_TYPE_KEY.MATCHING,
+    typename: 'MATCHING',
+    label: 'Matching',
+    id: 14,
+    autoGradable: true,
+    supportsPartialCredit: true,
+    manualGradingRequired: false,
+    disabled: true
+  },
+  {
+    key: QUESTION_TYPE_KEY.HOTSPOT,
+    typename: 'HOTSPOT',
+    label: 'Hotspot',
+    id: 15,
+    autoGradable: true,
+    supportsPartialCredit: true,
+    manualGradingRequired: false,
+    disabled: true
   }
 ] as const;
 
+/** Types actually offered in the product (excludes `disabled` ones with no DB row). */
+export const ENABLED_QUESTION_TYPE_REGISTRY = QUESTION_TYPE_REGISTRY.filter((type) => !type.disabled);
+
 export const QUESTION_TYPE_BY_KEY = Object.freeze(
   QUESTION_TYPE_REGISTRY.reduce(
     (acc, type) => {

packages/question-types/src/question-type-types.ts

@@ -8,4 +8,6 @@ export interface QuestionTypeMetadata {
   autoGradable: boolean;
   supportsPartialCredit: boolean;
   manualGradingRequired: boolean;
+  /** Built in code but not offered in the product (no `question_type` row). */
+  disabled?: boolean;
 }