Storing HOA decorations

For legalities, you should ask an attorney.

Was it legal/proper for the treasurer to keep the associations financial records at their home?
Was it legal/proper for the secretary to keep the associations records at their home?

Realistically, if the Association doesn't own or rent a storage area, or office, what is left is for volunteers to hold on to the items in their own homes.
This is typically done in an attempt to help the Association save money as climatized storage lockers can cost around $1,200 per year.

Unfortunately, this can result in issues of things being intentionally or unintentionally thrown out. Sometimes this is done with board approval. Sometimes it is done because nobody else volunteered the space in their homes.

Should the individual attempted to have other board members store the items prior to tossing them? Yes, of course they should have. Unfortunately, there is no real way of knowing if that happened or not.

My suggestion - support the shed. Make sure it is waterproof and (if possible) climatized. Perhaps volunteer to keep the items on your property.