fix: read activity shards in GET /api/feed; improve sync feedback

_merged/index.json is a shard manifest with activities:[] when the user
has >FEED_PAGE_SIZE activities. The endpoint now collects from all
index-{year}.json shard files before returning.

SyncResult gains a `total` field (activities received from server) so the
feed screen can distinguish "server returned nothing" from "all already
stored locally". Messages: "No activities on instance" / "Up to date (N)"
/ "X of N activities synced".

bincio/serve/server.py

@@ -537,13 +537,24 @@ async def get_token(login_req: LoginRequest, request: Request) -> JSONResponse:
 
 @app.get("/api/feed")
 async def get_feed(user: User = Depends(_require_auth)) -> JSONResponse:
-    """Return the authenticated user's activity summaries (mobile feed sync)."""
+    """Return the authenticated user's activity summaries (mobile feed sync).
+
+    _merged/index.json is a shard manifest (activities: []) when the user has
+    more than FEED_PAGE_SIZE activities.  Collect from all shard files.
+    """
     dd = _get_data_dir()
     user_dir = dd / user.handle
     for index_path in (user_dir / "_merged" / "index.json", user_dir / "index.json"):
-        if index_path.exists():
-            index = json.loads(index_path.read_text())
-            return JSONResponse({"activities": index.get("activities", [])})
+        if not index_path.exists():
+            continue
+        index = json.loads(index_path.read_text())
+        activities: list[dict] = index.get("activities", [])
+        for shard in index.get("shards", []):
+            shard_path = index_path.parent / shard["url"]
+            if shard_path.exists():
+                shard_doc = json.loads(shard_path.read_text())
+                activities.extend(shard_doc.get("activities", []))
+        return JSONResponse({"activities": activities})
     return JSONResponse({"activities": []})