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.