cĺient: Update to ESLint 9

- ESLint 9:
  https://eslint.org/blog/2024/04/eslint-v9.0.0-released/
  https://eslint.org/docs/latest/use/migrate-to-9.0.0

  - Lints current directory without any arguments:
    https://eslint.org/docs/latest/use/migrate-to-9.0.0#-change-in-behavior-when-no-patterns-are-passed-to-cli

- eslint-plugin-react-hooks:
  https://github.com/facebook/react/blob/eslint-plugin-react-hooks%405.0.0/packages/eslint-plugin-react-hooks/CHANGELOG.md

- eslint-plugin-react:
  https://www.github.com/jsx-eslint/eslint-plugin-react/pull/3759

- Prettier config not as necessary since ESLint 9 phased out stylistic lints:
  https://www.github.com/prettier/eslint-config-prettier/issues/290

  But there are some rules that are still enabled by recommended `@eslint/js` config.
  It is possible to check them with `npx eslint-config-prettier js/index.js`.
  In our case `no-unexpected-multiline` is still enabled:
  https://github.com/prettier/eslint-config-prettier/tree/v9.1.0#special-rules