generate fails if self.serverapp.root_dir not writable

[jhgoebbert]

Hello and thank you for this great extension 👍

Description

We are facing a Permission denied-issue when jupyter-ai is asked to generate a notebook.
It tries to generate the file in the directory set by self.serverapp.root_dir which is not writable.
https://github.com/search?q=repo%3Ajupyterlab%2Fjupyter-ai%20root_dir&type=code

Reproduce

If one starts a JupyterLab on a multi-user-system and wants to be able to browse all files this is set to
c.ServerApp.root_dir = '/'
Of course this root_dir is not writable and so jupyter-ai fails with Permission denied.

Possible solution

Instead of self.serverapp.root_dir the current directory of the filebrowser could be used.
(perhaps similar to the jupyterlab-git extension?)

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