I think not specifically "tree of life"... those are more usually dominated by one central tree within the overall design. More generically, I would say it's a "garden of paradise" design, symbolic of heaven. Those may also have a tree of life within the design but, again, most usually a single tree dominating at the centre.
It's a beautiful thing but values vary enormously according to age (modern rugs can still be valuable) and the weave in knots per inch (the more the better). Those are not things that can be determined from your photographs and I would suggest you get it professionally appraised. Presumably you have no provenience or provenance for it.
Yes, I know... but the internet is of full of vendors using descriptions which are not necessarily entirely accurate. Rugrabbit is a hosting site for vendors to post items for sale, taking whatever the vendor says as the description for the listing.
It looks like my tree of life rug, the same elements are there. I dont know that there is a strict definition on these things. Value cant be assigned from pictures, it depends on where it was made, how it was made, what it was made from, the quality and the wear.
Compare the lines of the animals and foliage in OP’s rugs with the “antique Persian” website rug.. OP’s rug design looks like computerized enlargement - the shapes and figures are “pixelated” rather than organic.