feat(conversations): pre-SDK rows read from canonical messages, implied titles, markdown adopts them by first prompt

src/beaver_gateway/frontends/api/frontend.py

@@ -30,7 +30,7 @@ from sqlmodel import col, select
 
 from beaver_gateway.core import audit
 from beaver_gateway.core.auth import VALID_SCOPES, hash_token
-from beaver_gateway.core.conversations import SEEDS
+from beaver_gateway.core.conversations import SEEDS, implied_title
 from beaver_gateway.core.kinds import Kind, as_kind
 from beaver_gateway.frontends._auth import require_token
 from beaver_gateway.frontends._sse import (
@@ -215,10 +215,14 @@ def build_app(runtime: GatewayRuntime, *, memory_root: Path | None = None) -> Fa
             limit=query_int(request, "limit", 200),
         )
         latest = await conversations.queue.latest(cast("int", r.id) for r in rows)
+        firsts = await conversations.first_user_texts(
+            cast("int", r.id) for r in rows if not r.title
+        )
         return {
             "conversations": [
                 {
                     **conversations.public(r),
+                    "title": r.title or implied_title(firsts.get(cast("int", r.id))),
                     "last_item": _queue_item(latest.get(cast("int", r.id))),
                 }
                 for r in rows