chore: Update svelte-kit, vite, and related npm deps in chat-app (#1473)

# Description

This PR is a followup to #1460 but with correct updates to
`package.json` and `package-lock.json`, and updates svelte-kit, vite,
and related npm dependencies in
https://github.com/GoogleCloudPlatform/generative-ai/tree/main/conversation/chat-app.

- [x] Follow the [`CONTRIBUTING`
Guide](https://github.com/GoogleCloudPlatform/generative-ai/blob/main/CONTRIBUTING.md).
- [x] You are listed as the author in your notebook or README file.
- [x] Your account is listed in
[`CODEOWNERS`](https://github.com/GoogleCloudPlatform/generative-ai/blob/main/.github/CODEOWNERS)
for the file(s).
- [x] Make your Pull Request title in the
<https://www.conventionalcommits.org/> specification.
- [x] Ensure the tests and linter pass (Run `nox -s format` from the
repository root to format).
- [x] Appropriate docs were updated (if necessary)