Armours stand cannot be picked up at all. Trying to interact with them just swaps out the amour as usual. I can pick up other mobs just fine.
I'd like to pick them up for the same reason as chests; to be able to quickly relocate them nearby without having to cluter my inventory.

Minecraft 1.21.4
Fabric Loader 0.16.9
Fabric API 0.110.5
Carry On 2.3.0
No other mod involved