[Task](oauth): Migrate to vite-react-ts eslint config and modern jsx

[ArtieReus]

Task Description

Update the oauth package's ESLint configuration to use the vite-react-ts config and migrate to the modern JSX transform, following the pattern established in #1975.

Sub-tasks

• Update eslint.config.mjs to use @cloudoperators/juno-config/eslint/vite-react-ts.mjs
• Change "jsx": "react" to "jsx": "react-jsx" in tsconfig.json
• Remove import React from 'react' statements from files that don't explicitly use the React object
• Keep React imports only where React APIs are directly referenced (e.g., React.useState, React.useEffect)
• Run pnpm lint to verify linting passes
• Run pnpm build to verify builds pass
• Run pnpm typecheck to verify type checks pass
• Run pnpm test to verify all tests pass

Related Issues

• Parent issue: [EPIC](apps): Migrate to Clean TypeScript ESLint Configuration #1565
• Reference PR: chore(template): migrate to vite-react-ts eslint config and modern jsx #1975

Additional Context

This migration updates the package to use the standardized vite-react-ts eslint configuration and enables the modern JSX transform introduced in React 17, which eliminates the need to import React in every file
that uses JSX.