Redstone can be placed on Top Slabs but no on Bottom Slabs, even tho it wouldn't exceed a full block's worth of space.

Would be super cool as Carpet already allows for Pushable Block Entities, having Redstone on Bottom Slabs would be a great addition!

That wouldn't be compatible with a vanilla client/server, and Carpet servers are accessible by vanilla clients and worlds loaded with Carpet compatible with vanilla servers.

you can't have two blocks in the same space. You can have two liquids, but redstone is not a liquid. Feels weird. I bet there are dedicated mods to do that.