Once upon a time, Lord Shiva, along with Bhagwati Durgā/Parvati

To prove my answer, I would like to present some extracts from Mahabhāgwat Purān I recently bought. Once upon a time, Lord Shiva, along with Bhagwati Durgā/Parvati , was wandering on a temple situated at the pleasant peaks of Mount Kailāsha. Seeing the most beautiful form of Parvāti, Lord Shambhu thought in his mind “Female birth is really fantasizing “. Then touching the lotus face of the Dēvi by his hands, who is beautiful in all Her limbs, spoke in His love-filled sweet tone- Shiva said- “ Oh Durgē, by your grace all of my wishes are fullfilled , now there is nothing left to ask for. But oh Sharvāni , I have one another wish. Oh Shivē, If you are graceful on me, please fulfil it as well. Dēvi Said- “ Oh Shāmbhu ,you are my beloved, what other desire you have, express it, I will fulfill as well. ” Shiva said- “ Oh Dēvi, if you are appeased with me, so, at my request, take birth anywhere on earth assuming a male form , and I will incarnate in form of a female. Like this time, that I am your beloved husband , and you are my wife, who is dearer to me than my life, this domestic-love will continue to prevail at that time as well. Oh Dēvi who is the fulfiller of desires of Her devotees, please , fulfil my this desire. Dēvi said - “ Mahadēva, Lord, for your pleasure , I will take birt as Krishna in the house of Vasudēva. And oh three eyed one, for my delight , you take a feminine birth.” Shiva said- “Oh Jagadhātri Shivē, for begetting you in male form, I will take the form of your beloved Radhā , the daughter of Vrishbhanu and roam with you. My eight other partial incarnations will be beautiful-eyed Rukmini, Satyabhāmā, and other asthā-bhāryās, who will incarnate in earth. So, yes, Rādhā was an avatar of Shiva. Before someone comes to quarell in the comment section that, Rādhā-Krishna are forms of Lakshmi-Nārāyan, I would like to quote a point as well. “Oh great sage, The Lord of Universe ,Lord Vishnu, at a different aeon, incarnates on Earth as Krishna in his full-form after getting boon from Me(Shiva) ,and oh wise one, will deliver this earth of burden of sins. Oh Sage, the one who hears or recites the tale of Jagadambikā incarnating as Krishna , gets all worldly pleasure and gets the final refuge of the Dēvi ‘s feet, which is inaccessible even for the Dēvās.” So when Lord Vishnu incarnates as Krishna in a different Kalpa, Lakshmi incarnates as Rādhā. Hope the question is duly answered. Jai Maa Durgā Har Har Mahādēv