Honestly, I've bounced off a lot of furry books that just feel like visual descriptors slapped onto generic plots. But the ones that stick are the ones where the 'otherness' of the characters is woven into the fabric of the world. The 'Monstress' comics are top-tier for this—the lore around Arcanics and Ancients is dense and feels mythic, not just window dressing for a cat-girl protagonist.
If you're looking at prose, Kyell Gold's 'Out of Position' series surprised me. It's contemporary sports romance on the surface, but the way it handles interspecies politics, historical tensions, and social integration between wolves, foxes, big cats etc., adds so much weight. The world feels lived-in because the 'furry' aspect directly impacts the conflict, not just the aesthetics.
Adrian Tchaikovsky's 'Dogs of War' isn't marketed as furry, but its bio-engineered animal soldiers are the most profound exploration of non-human consciousness I've read. The world-building about their creation and their place in human society is brutal and brilliant. That's the bar for me: when the lore makes you question what 'personhood' even means.