Two separate questions get mixed up here: (1) what can I legally do with this song, and (2) do I 'own the copyright' in the traditional sense. For creators, the first matters most day to day.
Usage rights vs copyright
The licence from your AI tool is what tells you whether you can publish, monetise and distribute a track. On Autunes, paid plans grant commercial usage. Whether AI output qualifies for traditional copyright protection is a separate, evolving legal question in many jurisdictions.
Be practical and honest
Because the law is still catching up, the safe approach is to use a paid plan with clear commercial terms and keep your prompts and lyrics on record. This article is general information, not legal advice — consult a professional for your specific situation.