Support `extra_headers` at inference time

[GabrielBianconi]

Combining #1192 + #1444.

[GabrielBianconi]

We need this to support Helicone.

[oliverbarnes]

Just a heads up that I started work on this - it's a nice segue to #1638, where I got familiar with extra_body.

I went through the two PRs mentioned in the description, all seems clear. Here's the plan for adding what's missing for extra_headers in comparison to the extra_body implementation:

1. Create types for inference-level headers (like UnfilteredInferenceExtraHeaders)
2. Add a database migration to store headers in ClickHouse
3. Update all client interfaces to accept header parameters
4. Modify the request flow to pass the extra headers through the entire stack
5. Add filtering logic for headers based on variant/provider
6. Add e2e tests for inference-level headers

(please let me know if anything seems off or is missing from the above)

[GabrielBianconi]

Thanks @oliverbarnes !