Add the layout restorer

[brichet]

Adds the layout restorer, to restore the state of the side/down panels.
It includes the current widgets opened in each panel, and the size of the panels.

record-2025-10-17_20.16.35.webm

Fixes #6990

User facing change

• save and restore the layout, only for the Notebook view, since it is the only one with side and bottom panels
• use only one workspace (unlike Jupyterlab), to avoid confusion. This means that changing the layout in one Notebook will affect the layout of other Notebook if they are reloaded. This workspace file is save in the jupyterlab workspace directory (.jupyter/lab/workspaces) and is named nb-default.

Code changes

• add the RestoreLayout and SaveLayout function to the shell, which uses some dedicated function to "dehydrate" and "rehydrate" the shell
• adds 2 plugins:
  • '@jupyter-notebook/application-extension:layout', which handle the shell layout restoration
  • '@jupyter-notebook/apputils-extension:state', which was previously activated from jupyterlab. Providing our own IStateDB allow to avoid some side effect, that the tab title update (which does not work correctly in Notebook, see Add the layout restorer #7747 (comment))

[github-actions]

👈 Launch a Binder on branch brichet/notebook/restorer

[brichet]

EDIT this error has been fixed

There is a conflict on the title of the browser tab with this PR.

BEFORE THE PR

record-2025-10-21_11.29.54.webm

AFTER THE PR

record-2025-10-21_11.30.28.webm

The tab title is not updated correctly anymore, probably because of https://github.com/jupyterlab/jupyterlab/blob/21f9c73298d7a450dba9927d404c87aae3011f7a/packages/apputils-extension/src/index.ts#L462-L469.
The code above wasn't called before this PR because there was no window resolver. It is required in this PR to allow saving the layout.

Maybe we should provide the IStateDB token in Notebook too.

[brichet]

Maybe we should provide the IStateDB token in Notebook too.

Added in c1b056e