Claude Desktop keeps each Code session under the folder of the account you were signed into. There is no account field inside the session, only the folder. Sign into a different account and every conversation is still on disk, intact, and invisible.
The transcripts themselves belong to no account; only a small card has to exist in the right folder. homecoming writes those cards into the account you use now, so the sessions show up in its sidebar, and records each one so it can take them out again.
It is an independent command-line tool for Windows. It is not affiliated with, endorsed by, or supported by Anthropic; "Claude" and "Claude Desktop" are Anthropic's names.