server/common: Fix response_format: json_schema & prefill parsing bug

[roj234]

Overview

The problem happens when you prefill json schema on Gemma4 (maybe other model),

bnf = ... root ::= start (thought | )? "```json" space response-format-schema space "```" ...
generation_prompt = <|turn>model <|channel>thought <channel|>{"name":

It could not parse because 3-backtick + json is missing

Fixes #23990

Automatically insert const string in BNF grammar thought to response-format-schema
Also changed struct server_task and task_result_state to share chat_parser_params

generation_prompt_fixed = <|turn>model <|channel>thought <channel|>```json {"name":

Additional information

This is a draft because

• share chat_parser_params might cause concurrent bugs, and
• common/json_schema_prefill_support.hpp mostly written by AI, this BNF string parser is very naive.

But IT RUNS now, if you (viewer, not contributor or owner) need this, cherry-pick it!

Requirements

• I have read and agree with the contributing guidelines
• AI usage disclosure: YES

[aldehir]

Tell your little AI buddy to simply prepend the backticks when constructing the generation prompt on continuation and report back the LOC difference.