Add providers module: one app on the real OpenAI, Anthropic and Gemini Spring AI models against a local server in three wire formats; options, prompt caching, cost from price sheets, failover with retry layers measured

Co-Authored-By: Claude Sonnet 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01JXVi2GMQ7bR5EmbUFdDj7N

providers/output/02-options.txt

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+# Options: portable, provider-specific, and the per-call trap
+
+A. ChatClient.options(ChatOptions.builder().temperature(0.2).maxTokens(200)) on each provider
+  OPENAI    model=gpt-6.1-sol, max_tokens=200, temperature=0.2
+  ANTHROPIC max_tokens=200, model=claude-sonnet-5-5, temperature=0.2
+  GEMINI    temperature=0.2, topP=1.0, maxOutputTokens=200
+
+B. Provider-specific options through the same ChatClient call
+  OPENAI    reasoningEffort + promptCacheKey -> prompt_cache_key=tickets-v1, reasoning_effort=low
+  ANTHROPIC topK(5)                          -> top_k=5
+  GEMINI    thinkingBudget(0)                -> generationConfig {"temperature":0.7,"topP":1.0,"thinkingConfig":{"thinkingBudget":0}}
+
+C. The trap: one built ChatOptions object handed to Prompt, then model.call(prompt)
+  OPENAI    ClassCastException (DefaultChatOptions cannot be cast to OpenAiChatOptions)
+  ANTHROPIC no error; model sent "claude-haiku-4-5", max_tokens 4096, temperature absent
+  GEMINI    ClassCastException (DefaultChatOptions cannot be cast to GoogleGenAiChatOptions)
+
+D. The other trap: OpenAI-specific options sent to the other two models
+  ANTHROPIC no error; model sent "claude-haiku-4-5"
+  GEMINI    ClassCastException (OpenAiChatOptions cannot be cast to GoogleGenAiChatOptions)