peptide storage: fridge, freezer, or neither? it depends which state it's in
There are really two storage questions and mixing them up is where most of the confusion comes from.
Powder (lyophilized, not mixed yet): freeze drying removed the water that hydrolysis needs, so it's comparatively stable. Cool and dark helps, freezing helps more for long horizons. Room temp for a limited period is generally tolerated, which is why shipping works at all.
Mixed (in solution): now there's water and two clocks start, chemical degradation and microbial risk. Fridge slows both. This is the state that actually needs care.
Freezing a mixed solution is usually a bad idea, which surprises people who assume colder is always better. Freeze thaw cycles cause mechanical stress, concentration changes at the ice interface, and can drive aggregation. A peptide that's fine frozen as powder may not be fine frozen in solution. If you have to, single use aliquots avoid repeat cycling.
Light and shaking matter too and get ignored. Some peptides are photosensitive. Shaking hard can denature, which is why the advice is to run the water down the side of the vial and swirl instead.
General formulation chemistry. Compound specific stability data is thinner and where it exists it should override all of this.