enh(#765): refactor `refreshHandler` and session refreshing; fix refresh provider refreshing

[phoenix-ru]

🔗 Linked issue

765

❓ Type of change

• [ ] 📖 Documentation (updates to the documentation, readme or JSdoc annotations)
• [x] 🐞 Bug fix (a non-breaking change that fixes an issue)
• [x] 👌 Enhancement (improving an existing functionality like performance)
• [ ] ✨ New feature (a non-breaking change that adds functionality)
• [x] 🧹 Chore (updates to the build process or auxiliary tools and libraries)
• [x] ⚠️ Breaking change (fix or feature that would cause existing functionality to change)

📚 Description

In #715 we introduced custom refresh handlers. Here I improve on it, introduce refresh function to CommonUseAuthReturn and properly use it for refresh handler.

📝 Checklist

• [x] I have linked an issue or discussion.
• [ ] I have added tests (if possible).
• [x] I have updated the documentation accordingly.