[rust] add streaming ui

[ecklf]

Description

Add streaming UI to axum example

Demo URL

Type of Change

• New Example
• Example updates (Bug fixes, new features, etc.)
• Other (changes to the codebase, but not to examples)

New Example Checklist

• 🛫 npm run new-example was used to create the example
• 📚 The template wasn't used but I carefuly read the Adding a new example steps and implemented them in the example
• 📱 Is it responsive? Are mobile and tablets considered?