Sugar pastes need to be stored at room temperature, away from heat and humidity.
Keep them in airtight containers (or grip seal bags), otherwise they will dry out.
Sugar pastes left in bags dry out quicker than those stored in airtight containers.
Don’t wrap the pastes in cling film. It is porous, so it doesn’t prevent the paste from drying out.
I use small baby food containers to store the coloured leftovers:
I put those pots in a large flat box, so it’s easy to find the colours. I try to use the pastes up as quickly as possible.