Watership Down by Richard Adams deserves a mention I think. It’s not exactly a series, but it did get a sequel. Richard Adams also wrote The Plague Dogs and Shardik. Shardik doesn’t actually take the POV of the animals, but Lord Shardik is a mythical bear that is kind of a main character. I haven’t read The Plague Dogs yet, and only learned about it while checking my spellings for this comment, but everything else.by Adams that I’ve read has been amazing.

Redwall book series

But I read them back when I was a kid. Not sure how it holds up to adult readers

A Night in the Lonesome October - Roger Zelazny… this is almost exactly what you are asking for.

Iron Druid chronicles has a small bit of it.

White Fang and Call of the Wild are classic examples of it.

Watership Down by Richard Adams

Fifteen Dogs kind of fits. It’s about a bunch of dogs that gain human intelligence and what they do with it.

Only adult one I can think of is Tailchaser’s Song by Tad Williams (cats). There’s a ton of these for kids, though; here’s a few I’ve read:

• Redwall series by Brian Jacques (forest critters; I found it repetitive after the first few, but ymmv)
• Mrs. Frisby and the Rats of NIMH by Robert C. O’Brien (rats)
• Stewart Little by E.B. White (mouse)
• Charlotte’s Web by by E.B. White (pig)

Edit: Sorry, I derped on the scifi/fantasy/action aspect of the request; the E.B. White books don’t fall into that category.

Hollow Kingdom by Kira Jane Buxton is amazing, although the follow up isn’t as good.

Adrian Tchaikovsky’s Children of Time is also amazing, though, again, the follow up isn’t as good.

If singular books are OK, there’s Ka: Dar Oakley in the Ruin of Ymr by John Crowley.

I could give more titles because I love books from the animal perspective, but these are my sci-fi/fantasy recs. I also second Watership Down.