Hello. I cannot craft any of the items in the mod, and when I click on them in REI nothing shows up.

Interesting, just checked in my own testing environment and everything seemed in order. Can you send me a log file when you get the chance?

I also attached a quick build with some small updates if you want to give it a shot, though I don't think it will fix your issue (Unzip the file, the jar is inside)
1.16.5-storagecabinet-1.2.0.zip

I will try. I have a lot of mods, so I don't know how helpful it will be!