Movable chests and anvils

In the Bedrock Edition of Minecraft, you are able to push 'Tile Entities' (Chests, Ender Chests, Barrels, Furnaces, Anvils, ect.) with pistons, but in the Java Edition, you cannot. Also, it would be good if the already existing immovable block of the Reinforced Deepslate would drop when broken with a diamond pickaxe and be craftable, perhaps with regular deepslate and/or smooth basalt/tuff and bone or iron blocks.

Thank you!