[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

[github-actions]

Hi, we're sending this friendly reminder because we haven't heard back from you in 30 days. We need more information about this issue to help address it. Please be sure to give us your input. If we don't hear back from you within 7 days of this comment, the issue will be automatically closed. Thank you!

[prise6]

Still an issue... and it's sad you don't fix it.