Agent memory without a vector database means the agent reads from a store you already keep current, not a new one you have to feed. Most projects build something new: a vector DB, a bespoke framework, a fresh pile of markdown only the agent sees. Your task app is none of those. You keep it fed without trying.
You already maintain a knowledge base by hand. Every day. It has your deployment runbook, the decision you made about that client, the reason you abandoned an approach in March. It is sorted into projects, tagged, dated, and pruned. Nobody calls it agent memory. That is exactly what it is.