I have no great issue with the Erdtree Avatar being the Asylum Demon, or other cases of enemies from previous games being given a new appearance and some tweaks. For that one in particular, it's been multiple games since we saw its animation set, so it seems more of a 'huh how about that' than a real negative point against the game.
That point applies to weapon movesets too - they've been refined and changed around in some cases, but many of those movesets are still fundamentally recognizable as ones from earlier entries. Again, I don't see that as a big issue - on some level it would disappoint if the fundamental stuff was changed beyond recognition.
However, I think it's important to make a distinction between repurposing assets from previous games, and reusing assets within the same game. Particularly in the case of Elden Ring since it does both, and by extension the conversation around the topic touches on both as well.
The most obvious case for this is the catacombs - dungeon after dungeon of the same boxy grey rooms and limited enemy set. The caves also suffer from this, though less so by virtue of being more natural environments that are harder to pick out as duplicates. I was noticing those by the latter half of my first (very much not 100%) playthrough, but now I'm on my second it's becoming a lot more obvious.
Reused bosses are also an issue - Ulcerated Tree Spirit is an intense and memorable encounter the first time round, but is cheapened the second, third, fourth, etc times you encounter it elsewhere. That goes doubly for bosses like Astel, Naturalborn of the Void - a unique mainline-tier boss that reappears in an overworld dungeon later on, with seemingly no precedent outside of needing something to put in the boss room.
Overall it's not a deal breaker given that ER is the most well-crafted open world I've seen, but my preference is and always has been for unique content, even if it's at the cost of volume.
It comes down to that feeling of something being cheapened by repetition - consider the difference between a weapon in Devil May Cry and a weapon in Diablo. In Devil May Cry, each weapon in completely unique in design, moveset and - in some cases literal - personality; finding one and using it feels special and distinct. Conversely, a weapon in Diablo is literal pocket change - the fact that it's a Broadsword of Greater Ass Whooping doesn't matter because there are a potentially infinite number of Broadswords of Greater Ass Whooping to be found; the excitement comes from the stats and effects it acts as a vehicle for rather than being intrinsic to the item itself, and thus the item itself ceases to matter.
Generalize that idea up to assets, level layouts, bosses, whatever you like, and you get the idea.