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>

src/scribe/services/plugin_context.py

@@ -27,7 +27,11 @@ from scribe.services import projects as projects_svc
 from scribe.services import shape_ledger as shape_ledger_svc
 from scribe.services import snippets as snippets_svc
 from scribe.services.access import label_shared_items, owner_names_for
-from scribe.services.embeddings import semantic_search_notes, semantic_search_rules
+from scribe.services.embeddings import (
+    document_title,
+    semantic_search_notes,
+    semantic_search_rules,
+)
 from scribe.services.lessons import LESSON_NOTE_TYPE
 from scribe.services.note_usage import record_surfaced
 from scribe.services.rule_usage import record_rule_surfaced
@@ -88,8 +92,10 @@ def _menu_name(title: str | None, note_type: str | None, data=None, body: str |
 def _menu_passage(title: str | None, chunk_text: str | None, name: str = "") -> str:
     """The matched chunk on one line, without the title it was embedded under.
 
-    Every chunk is `title\nsection` (`embeddings.embedding_text`), so the title
-    prefix is stripped exactly. A chunk that WAS only the title — a short
+    Every chunk is `title\nsection` (`embeddings.embedding_text`), and `title`
+    here must be the EMBEDDED one (`embeddings.document_title`) — for a snippet
+    or lesson that is `name — trigger`, not the stored name — so the prefix is
+    stripped exactly. A chunk that WAS only the title — a short
     record, or the head chunk of one — matched on the title, and for a
     trigger-keyed kind the part of it the name line no longer shows is the
     trigger: that is returned, because it is precisely what matched.
@@ -1235,7 +1241,10 @@ async def build_autoinject_hint(
         # queries and so are not in this search's report. No fallback to the
         # body's opening: on a menu that would be a line of preamble dressed as
         # a reason, and a reader cannot tell the two apart once indented alike.
-        passage = _menu_passage(note.title, (menu_chunks.get(nid) or {}).get("text"), name)
+        passage = _menu_passage(
+            document_title(note.title, note.note_type, note.data, note.body),
+            (menu_chunks.get(nid) or {}).get("text"), name,
+        )
         if passage:
             lines.append(f">   ↳ {passage}")
 
@@ -2324,6 +2333,10 @@ async def build_write_path_hint(
                         # (#4364): the line is built from facts, not from
                         # re-reading its own marker.
                         "name": _menu_name(note.title, note.note_type, note.data, note.body),
+                        # What its chunks are prefixed with, for stripping.
+                        "doc_title": document_title(
+                            note.title, note.note_type, note.data, note.body,
+                        ),
                         "seen": int(note.id) in excluded,
                         # Carried, not re-read off the rendered marker. The
                         # marker is prose assembled for a human and it already
@@ -2510,7 +2523,8 @@ async def build_write_path_hint(
         if item.get("seen"):
             continue
         passage = _menu_passage(
-            item.get("title"), (wp_chunks.get(int(item["id"])) or {}).get("text"),
+            item.get("doc_title") or item.get("title"),
+            (wp_chunks.get(int(item["id"])) or {}).get("text"),
             item.get("name") or "",
         )
         if passage: