common/parser: add proper reasoning tag prefill reading (#20424)

* Implement proper prefill extraction

* Refactor cli parameters, update docs, move reasoning budget sampler part to common/reasoning-budget.cpp

* Update tools/server/server-task.cpp

* refactor: move grammars to variant, remove grammar_external, handle exception internally

* Make code less C++y

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

models/templates/Apriel-1.6-15b-Thinker-fixed.jinja

@@ -7,7 +7,6 @@
 {%- set available_tool_string = '' -%}
 {%- set add_tool_id = true -%}
 {%- set add_thoughts = true -%}            {# whether to include <thinking> reasoning blocks #}
-{%- set add_generation_prompt = true -%}      {# whether to emit reasoning starter before assistant response #}
 {# Optional token placeholders (safe defaults) #}
 {%- set bos_token = bos_token or '' -%}
 {%- set eos_token = eos_token or '' -%}