While there is no doubt the mAnasakhaNDa is a peripheral attachment to the skandapurANa, IMO it is hard to give it a precise date. Likely something medieval. However, that does'nt make kailAsa and mAnasarovara as purely mythical or unassociated with the current tIrtha. https://twitter.com/shrikanth_krish/status/1348423258933231616

First, I'd mention a non-Sanskrit source the tamiL periyapurANam which talks of the nAyanmAr appar's physical journey to kailAsa where he bore great hardship -- it clearly describes a difficult trek.Implying a physical location. Next other purANa-s like matsya & vAyu also mention

the pilgrimage to kailAsa and the existence of a great lake sometimes called mandAkinI: this does correspond well the current kailAsa. This fact is even recorded by the Mohammedan scientist al Beeroonee who had a generally negative view of the H.He mentions the lakes near kailAsa

as a spot of great holiness to the H. Then, we have the nirgrantha-s who consider it the nativity spot of their first ford-maker. They have texts with a tIrthayAtra prescription to the mountain including parikrAma along with austerities. The Tibetans refer to the same mountain as

kailAsa, and it was already known in the pre-bauddha more H-like natural religion of the Tibetans, the Bon religion. Then in the bauddha yoga and yoginI-tantra phase it came to be seen as the abode of chakrashambara, a deity modeled after shiva of the sanAtana-dharma. Then the

famed kAlachakra tantra in its prognostication holds that rudra-chakravartin kalkin would joined by the gods in the kailAsa region to relieve the world of the monstrous oppression of the Abrahamists at the end of the yuga. Thus, generally, the identification of the tibetans &

H align suggesting that mAnasarovara and kAilAsa of today were generally considered to be those sites by the votaries of the Indian religions.