ثُمَّ يُلَبِّي عَقِيبَ صَلَاتِهِ
Translation: Then one pronounces the talbiyah after the prayer.
ʿAqība ṣalātihi indicates following the prayer. The passage gives an orderly preparation: prayer, supplication and then talbiyah.
Hanafi fiqh discusses entry with intention plus talbiyah or a recognised substitute remembrance. Garments or bathing must not be equated with the entry formula.