Feature: allowing users to access the raw provider responses

[njbrake]

The change makes sense, considering our current approach of sticking to the imposed OpenAI "standard".

It's not a blocker but as followups would be nice to:

• test against the real Anthropic API with cache settings
• have a discussion about the option of allowing users to access the raw provider responses

Originally posted by @daavoo in #750 (review)