Is prayer after the supplication of one who stirs at night recommended or obligatory to complete the noble Hadith?

The hadith (definition) narrated by Al-Bukhari from Ubadah ibn Al-Samit (may Allah be pleased with him) states that the Prophet (peace be upon him) said: "Whoever awakens at night and says: 'La ilaha illallah wahdahu la sharika lah, lahul mulku wa lahul hamdu, wa huwa ala kulli shayin qadir. Subhanallah, walhamdulillah, wa la ilaha illallah, wallahu akbar, wa la hawla wa la quwwata illa billahil aliyyil azim (There is no god but Allah alone, He has no partner. To Him belongs sovereignty and to Him belongs praise, and He is over all things competent. Glory be to Allah, and praise be to Allah, and there is no god but Allah, and Allah is the Greatest. There is no might or power except with Allah, the Most High, the Most Great),' then supplicates: 'Rabbi ighfir li (My Lord, forgive me),' he will be forgiven." Al-Walid said: "Or he said: 'he supplicated, and it was answered.' "Then if he gets up, performs ablution, and prays, his prayer will be accepted." Therefore, it is hoped that supplication and praise of Allah will be accepted even if one does not perform ablution or pray.