[vscode] Use `biome ci` instead of `eslint`

[c-bata]

Contributor License Agreement

This repository (optuna-dashboard) and Goptuna share common code. This pull request may therefore be ported to Goptuna. Make sure that you understand the consequences concerning licenses and check the box below if you accept the term before creating this pull request.

• [x] I agree this patch may be ported to Goptuna by other Goptuna contributors.

Reference Issues/PRs

Refs #831

What does this implement/fix? Explain your changes.

Use biome ci instead of eslint.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 69.60%. Comparing base (b8f013f) to head (4849fda). Report is 1 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #833 +/- ## ======================================= Coverage 69.60% 69.60% ======================================= Files 35 35 Lines 2375 2375 ======================================= Hits 1653 1653 Misses 722 722 ```

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