What is the ruling on one who does not supplicate to Allah during prostration, but rather praises Him instead, and is supplication obligatory during prostration?

Supplication during prostration (sujud (definition)) is recommended (mustahabb) but not obligatory. It is one of the positions where prayers are answered. Among the reported supplications for it are: "Glorious art Thou, O Allah, and with Thy praise, O Allah, forgive me," and "O Allah, help me to be grateful to You and to worship You in the best manner," and "My Lord, indeed I have wronged myself, so forgive me," and "O Allah, forgive me all my sins, the minor and the major, the first and the last, the secret and the public." The command has been reported to supplicate frequently during prostration because it is a place where prayers are likely to be answered. And whoever omits supplication during prostration, their prayer is still valid and there is no sin upon them.