Another question reminded me of two similar stories that I can't place regarding intelligent animals.
In the one I'm asking about in this question, there are various species of sapient animals in a far future Earth. Humans no longer walk the Earth -- they apparently all uploaded their consciousnesses into towering crystalline structures long ago, and if those uploaded minds are still conscious, they have had no apparent interaction with the external world for a very long time.
I don't remember whether the animals had been artificially uplifted or had evolved intelligence naturally, but if they possessed (as they seemed to) passed-down stories of what humans were, I would guess they had been at least more sapient already, when the last breathing humans vanished, than non-human animals are now.
The main character is a member of one of the species of sapient animals. I don't remember the story very well, I but remember a scene in which the main character is shocked by seeing a bear deliberately brush up against one of the crystalline structure pylons. This taboo act somehow leeches some psychic energy from the structure that houses the uploaded minds, conferring some extra intelligence or something like that.
I think there may have been another element to the story -- that the main character was in telepathic communication with an animal elsewhere on Earth. This might be a memory mixed in from some other story, however.
This story was probably in a science fiction magazine or anthology from the 1960s to early '00s.
It is not Edmond Hamilton's "Day of Judgment".
I do not think it is Andre Norton's novel A Breed to Come (which was a suggested answer to the question linked at the top), either. This was at most novella length, not a full book.