Add provider request diagnostics for repeated timeouts

[Hanjo92]

Problem\nUsers can see repeated provider request timeouts, but the extension currently reports only a generic timeout message. It does not show the resolved provider, sanitized URL, model, timeout budget, or elapsed time, making it hard to distinguish network connectivity, wrong OpenAI-compatible endpoint paths, unsupported models, and local Ollama availability.\n\n## Acceptance Criteria\n- Timeout and network errors include provider, model, sanitized target URL, timeout budget, and elapsed time.\n- Error messages avoid exposing API keys or request bodies.\n- OpenAI-compatible base URL handling remains tested.\n- Existing provider request tests continue to pass.