Subissue: Fix & add E2E tests for new chat commands framework

[dlqqq]

Problem

#161 broke several E2E tests for the old autocomplete framework, and lacks E2E tests for the new chat commands framework.

Proposed Solution

Update & fix all E2E tests pertaining to chat commands before Jupyter Chat v1.0.0.

Additional context

This isn't urgent as long as Jupyter Chat is still on major version v0.x. I'm not aware of any package other than Jupyter AI that is consuming this as a dependency.

[dlqqq]

Old autocompletion tests which we should port: https://github.com/jupyterlab/jupyter-chat/blob/73512c16a6c602b81f873ecf9a3c20cb73cefd94/ui-tests/tests/autocompletion.spec.ts