[fix] Update FastAPI example to use non-deprecated APIs

[AryanSharma48]

Problem

The FastAPI example currently uses the deprecated resilient_api and
ResilientConfig APIs.

These APIs have been replaced by smooth_api and SmoothConfig, but the
example has not yet been updated. Running the example therefore produces
deprecation warnings.

What needs to be done

Update examples/fastapi/main.py to use the current SmoothAPI APIs.

Specifically:

• Replace resilient_api with smooth_api
• Replace ResilientConfig with SmoothConfig
• Keep the existing example behavior unchanged

Acceptance Criteria

• examples/fastapi/main.py uses the current API names
• The FastAPI example runs successfully
• No SmoothAPI deprecation warnings are produced
• Existing endpoint behavior remains unchanged

Files to look at

• examples/fastapi/main.py
• packages/smooth-api-py/smooth_api/__init__.py

Prerequisites

Basic Python and familiarity with imports.

Notes

Please avoid making unrelated changes to the example.