common: Refactoring sampler parameters (#20429) (#22233)

This change refactors the reasoning_budget_message parameter from the
common params into the sampling parameters specifically. It also removes
the reasoning_budget common parameter and standardizes on the existing
reasoning_budget_tokens parameter in the sampling configuration.

Issue: https://github.com/ggml-org/llama.cpp/issues/20429
Original PR: https://github.com/ggml-org/llama.cpp/pull/20297

common/common.h

@@ -274,6 +274,7 @@ struct common_params_sampling {
     std::vector<llama_token> reasoning_budget_start;           // start tag token sequence
     std::vector<llama_token> reasoning_budget_end;             // end tag token sequence
     std::vector<llama_token> reasoning_budget_forced;          // forced sequence (message + end tag)
+    std::string              reasoning_budget_message;         // message injected before end tag when budget exhausted
 
     bool backend_sampling = false;
 
@@ -581,8 +582,6 @@ struct common_params {
     bool force_pure_content_parser = false;
     common_reasoning_format reasoning_format = COMMON_REASONING_FORMAT_DEEPSEEK;
     int enable_reasoning = -1; // -1 = auto, 0 = disable, 1 = enable
-    int reasoning_budget = -1;
-    std::string reasoning_budget_message; // message injected before end tag when budget exhausted
     bool prefill_assistant = true; // if true, any trailing assistant message will be prefilled into the response
     int sleep_idle_seconds = -1;   // if >0, server will sleep after this many seconds of idle time