[BUG] Input and output are not collected with Fast API engine in AML

[prise6]

Describe the bug
Promptflow server runtime with FastAPI doesn't write intput/output in collector.

How To Reproduce the bug
With v2 fastapi + managed online endpoint with Azure Machine Learning (AML), the data collector can't write anything because in FlowMonitor input_data are requested with input_data = self.context_data_provider.get_request_data(). This method looks for a key called input_data in FastapiContextDataProvider.
But the value of this key is None because we don't set it correctly in get_score_router()

code source: src/promptflow-core/promptflow/core/_serving/v2/routers/score.py

Expected behavior
Same behavior than Flask engine.

Additional context
I wrote a PR #3890