AAP-37878: move Chatbot test to vitest-browser-react

Right now, our tests are failing due to some problem with `happy-dom`, the fake webbrowser
used to run the tests by `react-testing-library`. `jsdom` is an alternative but we cannot
use it without adjusting our tests and facing similar issues or limitations.

By moving to `vitest-browser-react`, we are now able to run the tests against a real browser
like Chrome or Firefox. We still have the option to run the tests "headless" for a CI environment.

`vitest-browser-react` is directly based on `vitest-browser` and allow us to stay in a standard
`vite` ecosystem. It also reuses some elements from `react-testing-library`, which explains why
the PR is not that large.

Overall, this change reduces the differences between our tests and the production environment,
and allow use to limit our exposure to the limitations of these dummy browser implementations.