Storage Drawers will not break if I try to left-click from the top, bottom, or sides. And to clarify, I'm not trying to break it from the front, I know that left-clicking the front takes items out or whatever. I'm specifically trying to break it from the sides, and its not working. Am I missing a dependency? Or is a mod interfering with Storage Drawers? I'll leave the mod list below:

Additional Placements
AnvilRepairing
AppleSkin
AutoRegLib
Cloth Config v8 API
Cold Sweat
Create
Create Crafts & Additions
Create Enchantment Industry
Create Jetpack
Create: Steam 'n' Rails
Egg Generator
EntityCulling
Farmer's Delight
Ferrite Core
FramedBlocks
Fusion
GoProne
Infinite Lava
Just Enough Items
Kotlin for Forge
Memory Leak Fix
Moonlight Library
NoAddRepCost
Quark
Rechiseled
Rechiseled: Create
Rubidium
Storage Drawers
SuperMartijn642's Config Library
SuperMartijn642's Core Lib
Supplementaries
TimeControl

If you're referring to Creative mode, then yes, this is a known issue. Applies to 1.19.4 as well.
You can still break the drawer in survival mode however.

Unfortunately, the oldest version still supported is 1.20.1 at this point, so I'm not sure 1.19 bugs will get fixed anymore.
The bug has been fixed in 1.20.1 and newer.