The kittens give dusty cuddles and it's @catnet trying to pick that up.

The @dustbunny might come, too, it has the kittens on its watchlist. But that's not in any way related to the @catnet program or the Cat Appreciation Tokens.

You say you never see the bunny? That's weird, because the bunny tells me otherwise:

It must have visited you at least once in the past 24 hrs and multiple times during the past week. in total it has fluffed up dusty rewards of yours by a combined $2.025 since it started watching for your dust.

These and more stats are available on the bunny discord.

Can't tell you much about dusty, I'm not directly involved with them, that's @danielsaori's project. But they do have a discord, too, and I think you can check your stats there as well.