If Buddha is an incarnation then how do we understand his previous incarnations as animals mentioned in the Jataka tales?

From: rishit

Hare krishna prabhuji.Please accept my humble obeisances. my question is that :-  we know that Buddha was an incarnation of Lord  Vishnu. Yet from the Jataka tales we come to know that Buddha reveals he came in his earlier lives as a deer , a thief, a dog and many more.Is the information authentic. Again if this were true then in what categories do these avataras as a deer, theif or dog . Are they mentioned in shastras.

Transcript

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Question from Rishit Prabhu. We know that Buddha was an incarnation of Lord Vishnu, yet from the Jataka tales we come to know that Buddha reveals he came in his earlier lives as a deer, a thief, a dog and many more. Is the information authentic? Again, if this were true, then in what category do these avataras as deer, thief or dog fall? Are they mentioned in Shastras? Answer, Buddha, it is explained by Rupa Goswami in the Lado Bhagavata Amrita, is a Shaktyavesha avatar.
Shaktyavesha avatar means he is a Jiva who is given the extraordinary potency, the Avesha of Shakti by the Lord for doing some specific missions. That is why it is not that this is necessarily contradictory with the Jataka tales idea because as a soul, the person can come in various forms and that person is given Shakti by the Lord and that as a due to the Shakti given by the Lord, the person can exhibit compassion and do some extraordinary things in various incarnations. So, the Jataka tales contain certain morals which are taught and those morals are like preliminary principles of goodness so that people can gradually come towards spirituality and they are taught by Buddha.
So, we know that Buddha came for a specific mission of elevating people from ignorance towards somewhat level of goodness without bringing in the Vedas. So, Jataka tales serve that purpose. Now, in the Vedic scriptures themselves, there is not much description of Buddha’s previous or other incarnations.
But we have to understand that he is a Jiva who has been given that power by the Lord. So, as a Jiva, he can have come in many earlier lives. It is not necessary that every Shaktyavesha avatar has to descend directly from the spiritual world, come for one life and then go back immediately.
No, that person can be there for many lifetimes and doing various kinds of activities. So, these avatars are not mentioned in the Vedic scriptures but they are compatible with the understanding that the soul who is Shaktyavesha avatar as Buddha, that soul has earlier lives also. And Jataka tales as an authority to the extent that its teachings agree with the conclusion of the Vedic scriptures.
Thank you.