You might find this video interesting, if a little detailed:

It describes how to build strong, thin floating shelves.
I might recommend Cedar for cats. They seem to enjoy scratching on it.

Maybe something like this: [amazon.com]

It would need a 1" shelf thickness or better.

I agree with what others here have said, my cat loves her shelves but she jumps further and moth more force than I would have expected, make sure the shelves are securely mounted 20lb may not be enough for a 12lb cat

I received several 24 and 12 inch shelves as a gift. Mom bought them from Etsy. I had contractors install them. They opted to add substantial mounting brackets. They look great and are holding well. The cats use them heavily. I have no worries that they will come down. PM if you want to discuss details. Here are photos and link them on etsy. (If you search “cat furniture shelves” you can pull lots of options).

[etsy.com]

I would assume the cat jumping or landing could exert more than 6# of force. It might also matter where on the shelves it lands. If that is a low estimate to protect themselves, they might be fine, but if they are accurate, you may want to reinforce them.