Is purchasing studio equipment for recording songs considered aiding in sin and an ongoing sin, and how can one repent from that?

Assisting in the purchase of items used in unlawful singing is assisting in a sin, and the money earned from it is haram (unlawful). Sincere repentance to Allah Almighty is obligatory, involving remorse and a firm resolve not to return to such a sin. If you repent, Allah will accept your repentance, and the lingering effects of the disobedience will not harm you.