Deduplicate code across providers and core logic

The `dupl` tool identified 431 clone groups in the codebase.

Significant duplication was found in:
- Provider implementations (`anthropic`, `google`, `openai`, `openrouter`, `openaicompat`)
- `language_model_hooks.go`
- `provider_options.go`
- Core provider logic
- `agent.go`
- Test files (`*_test.go`, `providertests`)

We should refactor this code to use shared abstractions where possible to improve maintainability and reduce technical debt.