  In this paper we study 4d gradient steady Ricci solitons, which are weak
$\kappa$-solutions, and admit O(3)-symmetry. Under a weak curvature decay
condition, we find precise geometric asymptotics of such solitons, which are
similar to those for 3d compact $\kappa$-solutions found in [ABDS22]. This is
the first step towards the classification of 4d gradient steady Ricci solitons
and more general ancient Ricci flows.
