Preserve chats cross multiple machines under one account

### Feature summary

It would be nice to have my chats preserved as much as possible when logging into different machines using one account. They could be

### What problem are you trying to solve?

I have a dev laptop and a dev box. Sometimes I started to work from my dev laptop and later on figured out that I need to run some tests on my dev box. I would love to continue the conversation when I log in to different machines.

My dev laptop is a mac with arm. My dev box is a windows with x64.

### Proposed solution

Save the chat history under my account somehow.

### Workflow impact

_No response_

### Installation context

_No response_

### Additional context

_No response_

No files, tests, or implementation entry points are named in the issue. Start by mapping how the app currently stores chats and handles account data, then define the cross-machine persistence scope and acceptance criteria for continuing a chat across the stated macOS ARM and Windows x64 environments.

索引モデルが issue の本文から書いたものです。