Warden can detect the vibration of Wolf's sitting down and standing up on wool

I can confirm this issue.

But to be honest I'm a little bit regret to report this since I think asking Wolves standing up or sitting down is a kind of player-NPC interactions and has nothing to do with whether the Wolf is on Wool or not. Later of the testing I tried to ask for trade with a Villager who is standing on a Wool without professions and can still be detected by Warden. So it's more like, "Warden can detect the vibration of interactions between Player & entity which is on Wool."

The sensor detects the player interacting with the wolf.
Wool suppresses vibrations from an interaction between an entity and the wool.