Feature Request: Notebook automatically saves the results of the backend

Problem:
When running the note, refreshing the page or disconnecting the network will lost the latest running record after the page is reopened, which is very unfriendly for long-running tasks.

Any good idea to solve this?

No files, tests, or entry points are named. Start by reproducing a long-running notebook task, then refresh the page or disconnect the network and observe what is lost after reopening. Define the expected persistence behavior before locating the backend and notebook interface areas involved.

Written by the indexing model from the issue text.