You can output it as a memory using a simple prompt. You could probably re-use this prompt for any product with only slight modification. Or you could prompt the product to output an import prompt that is more tuned to its requirements.

e.g. https://claude.com/import-memory

This is one of the many reasons I don't think the model companies are going to win the application space in coding.

There's literally zero context lost for me in switching between model providers as a cursor user at work. For personal stuff I'll use an open source harness for the same reason.

I think this is more about which model you steer your coding harness to. You can also self-host a UI in front of multiple models, then you own the chat history.

I don't see any value in chat history. I delete all conversations at least weekly, it feels like baggage.

for me there is zero value there.