Ask HN: What is the best way to preserve, and continue to use chats in Claude?

I use Claude Ai frequently, the other day I was working on a project and got interrupted and came back to that chat a few days later, only to find it was not in my chat list. I did a search and Claude seemed to find part of the chat but not all of it. Then I realized how naive I have been in my usage. The chat history looked like it was keeping all these threads for me to reference and continue to work with - I was treating it like browser tabs in a way. But now I see many of my chats do not appear in the chat list and some are only partly recovered by search or at times even search does not find them. I have now looked around and find all kinds of ways to save the chats locally or on online services. I would like two core features 1) a record of all my chats saved so I can review them and search them. 2) there are many chats I would like to “park” and continue the conversation later, maybe that would be saving a conversation and using that as a prompt to carry on later?

How do you manage this? I’m finding that I am using Claude like a scratch pad for ideas, but it is like doing so with disappearing ink.