refactor(notes): a snippet's and lesson's stored title is its name; the trigger joins it only in the embedded document (milestone 427)

The title was `subject — trigger` because the stored title WAS the
embedded one, and the join is what makes these kinds rank on the
situation they apply to (#2485). Every surface that shows a title then
showed the trigger too -- menus, lists and search rows ran to kilobytes.

- embeddings.document_title(title, note_type, data, body) joins the
  trigger from `data` (body fallback) at embed time. Idempotent: an
  un-migrated composed title comes out the same, never doubled. The
  embed path, the startup backfill and the dedup gate's semantic signal
  all use it, so the embedded text -- and every vector -- is unchanged.
- Writers store the subject: snippet create/update (service, REST, MCP)
  and lesson_document. Both compose_title helpers are removed.
- Readers: dedup takes `data`; the menus strip the embedded title from a
  passage; list rows project `when_to_use`, which SnippetListView reads.
- 0108 rewrites existing rows on an exact `' — ' || <own trigger>`
  suffix with raw SQL, leaving updated_at alone so the backfill does not
  re-embed the corpus for identical vectors. Downgrade recomposes.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/test_lesson_write_path.py

@@ -117,7 +117,8 @@ async def test_the_duplicate_gate_runs_before_anything_is_created():
 @pytest.mark.asyncio
 async def test_the_gate_compares_the_composed_document_not_the_raw_fields():
     """What reaches the gate is the title and body a lesson will actually be
-    stored as. Comparing `what` alone would miss that the trigger is half the
+    stored as, plus the `data` its EMBEDDED title is built from (milestone
+    427). Comparing `what` alone would miss that the trigger is half the
     document, and would judge two lessons alike that rank nothing alike."""
     _user_id_ctx.set(7)
     gate = AsyncMock(return_value=None)
@@ -128,8 +129,9 @@ async def test_the_gate_compares_the_composed_document_not_the_raw_fields():
         await create_lesson(what=SUBJECT, when_to_apply=TRIGGER, insight="Look.")
 
     title, body = gate.await_args.args[1], gate.await_args.args[2]
-    assert title == f"{SUBJECT} — {TRIGGER}"
+    assert title == SUBJECT
     assert body.startswith(f"**When to apply:** {TRIGGER}")
+    assert gate.await_args.kwargs["data"]["when_to_apply"] == TRIGGER
     assert gate.await_args.kwargs["note_type"] == "lesson"
 
 
@@ -157,9 +159,11 @@ def test_a_lesson_is_judged_at_the_trigger_dominated_bar():
 
 @pytest.mark.asyncio
 async def test_an_update_recomposes_both_halves_of_the_document():
-    """A new trigger has to reach the title AND the head of the body. Patching
-    one would leave a lesson that reads correctly and ranks on the old
-    situation — the failure mode with no symptom."""
+    """A new trigger has to reach the mirror AND the head of the body — the two
+    places the embedded document reads it from (milestone 427). Patching one
+    would leave a lesson that reads correctly and ranks on the old situation —
+    the failure mode with no symptom. The title stays the subject, even when
+    the stored one was an un-migrated composed title."""
     _user_id_ctx.set(7)
     stored = _stub_note(
         title=f"{SUBJECT} — {TRIGGER}",
@@ -172,7 +176,7 @@ async def test_an_update_recomposes_both_halves_of_the_document():
         await lessons_svc.update_lesson(7, 1, when_to_apply="a guard goes red")
 
     fields = updated.await_args.kwargs
-    assert fields["title"] == f"{SUBJECT} — a guard goes red"
+    assert fields["title"] == SUBJECT
     assert fields["body"].startswith("**When to apply:** a guard goes red")
     assert fields["data"]["when_to_apply"] == "a guard goes red"