Show orange upload button when Strava/Garmin auth fails

GET /api/me/sync-status reads _strava_sync_status.json and
_garmin_sync_status.json for the logged-in user. On page load the nav
script checks this endpoint and, if either service has status=auth_error,
turns the upload arrow orange with a tooltip naming the disconnected
service(s).

bincio/serve/routers/me.py

@@ -317,3 +317,26 @@ async def me_change_password(
         raise HTTPException(400, "New password must be at least 8 characters")
     _change_password(deps._get_db(), user.handle, new_pw)
     return JSONResponse({"ok": True})
+
+
+@router.get("/api/me/sync-status")
+async def get_sync_status(
+    bincio_session: str | None = Cookie(default=None),
+) -> JSONResponse:
+    """Return the last sync status for Strava and Garmin for the logged-in user."""
+    user = deps._require_user(bincio_session)
+    user_dir = deps._get_data_dir() / user.handle
+
+    def _read_status(filename: str) -> dict | None:
+        p = user_dir / filename
+        try:
+            return json.loads(p.read_text(encoding="utf-8"))
+        except (OSError, json.JSONDecodeError):
+            return None
+
+    strava = _read_status("_strava_sync_status.json")
+    garmin = _read_status("_garmin_sync_status.json")
+    return JSONResponse({
+        "strava": strava,
+        "garmin": garmin,
+    })