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>