What I do currently is having a markdown file named MEMORY.md at the root folder. Then, whenever I create a new conversation with an agent, I refer to that file. That file becomes the initial source of context and knowledge. At the end of an task, before I leave the conversation, I ask the agent to update MEMORY.md with lessons and new knowledge it has gathered from our conversation, it also removes stale or outdated information from that markdown file.
I myself do not care what's written in that file, I steer, instruct and share my knowledge, visions, goal and preferences in our conversations, and the agent will boil that down and update the markdown folder. It has worked very well for me.
I now do not have to worry about creating handoff prompts when creating a new conversation or that I have to teach an agent from the ground up about the context we're in, I just refer to that markdown file.