Souls are not physical, there is nothing for science to prove. Science is the realm of the physical world. Not sure what you are referring to, but if you are referring to proof of the spiritual realm, no.
This is not really correct 1ke, or at least confusing.
It depends what you mean by “science” I suppose.
Proof involves the realm of reason (as opposed to faith).
Both philosophy and science belong to reason.
In pre-Enlightenment times any discipline that relied on reason was called a “science”.
That used to include Philosophy.
Just because the physical sciences may not be able to prove the existence of the soul that does not mean philosophy hasn’t - because in fact ancient science allegedly did.
The Church teaches that the existence of God can be proven (by the ancient science of natural philosophy) and the proof of the soul is of exactly of the same order. It really is a “scientific truth” in the mind of the Church.
The confusion is perhaps that we have been seduced by the secular Enlightenment which overthrew both Faith and Natural Philosophy which the Church continued to use from ancient times.
Modern science alone then became favoured as the only discipline capable of delivering helpful “proof”.
That is why the Church and the world today are at such odds. It was not always so, the educated world was once far more favourable to religion than it is today.
So has it been scientifically proven that animals have souls?
Yes it has, by the ancient science of natural philosophy.
(While souls are not themselves physical they influence the physical - therefore by these physical effects reason is able to make conclusions re their existence. The Physical sciences do not have the methodology or tools of reason needed to make this enquiry. They were discarded at the Enlightenment as unhelpful).
Do modern scientists accept this? No they don’t, because at the Enlightenment (when modern science arose) they rejected Natural Philosophy, thinking it was a form of Faith rather than true reason.
We Christians are still reeling intellectually from that divorce of our parents (the Church and our European Culture) that started around 400 years ago. It is still unwinding.