Very simply, Drawers from Functional Storage do not work on contraptions, either breaking off if normally glued, or stopping the contraption from forming at all if stuck on via a glued Linear Chasse. The Drawers are listed as Unmovable Blocks.
Minecraft Version: 1.21.1
NeoForge: 21.1.219
Functional Storage: 1.5.5
Create: 6.0.9
Smarter Contraption Storage: 6.0.0-1.4.5
Sidenote, I did just noticed that your mod seems to be listed for Create 6.0.0 writing this out. No crashes or anything, but not functioning properly with the other mod (which was the main draw for me)