fix: improve provider compatibility and preserve session history on retries

[seratch]

This pull request fixes multiple issues discovered through live integration testing:

• Preserves custom headers and existing HTTP configuration across provider adapters.
• Normalizes provider-specific function-tool response roles without affecting unrelated providers.
• Prevents non-streaming model retries from removing previously committed session messages, including SQLite-backed sessions.
• Adds regression coverage for provider configuration, function-tool responses, and session persistence across retries.