fix: types for `chrome-extension` package to be compatible

[PatrykKuniczak]

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Priority*

• [x] High: This PR needs to be merged first for other tasks.
• [ ] Middle: This PR should be merged quickly to prevent conflicts due to common changes. (default)
• [ ] Low: This PR does not affect other tasks, so it can be merged later.

Purpose of the PR*

I've described it in details here: https://github.com/Jonghakseo/chrome-extension-boilerplate-react-vite/issues/714#issuecomment-2341656789

Changes*

I've added vite and @types/node for chrome-extension package