Keeping and choosing are different.
One conversation can contain questions, experiments, quotations and directions you later abandon. Giving all of it to your next AI task is not the same as giving that task the right background.
Start with the current task.
First state what you are trying to do. Then choose the goals, constraints and decisions that affect the answer. The selected material should be inspectable and editable, with its source available to check.
Make past work usable.
PAIA is not designed to make you spend more time reading old chats. It is designed to bring expressions you have already created back into use. Saving is the starting point; reuse under your control is the purpose.