Feature Request: add per-request "reasoning" options in llama-server

[ngxson]

Feature Description

As reasoning models are becoming mainstream, we start to see some pattern:

• Most models use <think>, <reasoning>, etc, basically a set of known tokens now
• The "reasoning budget" can technically be supported by any models, not just Qwen, by keeping track of number of tokens between <think> and </think>
• "no think" is just a reasoning budget == 0

So I'm thinking about accepting an object like this for each request:

"reasoning": {
    "budget": -1, // number of reasoning tokens budget
                     default: -1 (inf) ; 0 for no think
    "format": "", // equivalent of --reasoning-format
                     if set to "deepseek", reasoning will be returned in "message.reasoning_content"
                     if set to "hide", it will be completely hidden
                     default: "none", return the reasoning with the message as normal
}

The reasoning format "hide" can be implemented via #13214 ; the "deepseek" format current only supported for non-stream, but I think we can modify a bit to support this.

For the budget, we don't yet have the logic to handle it.

[GreenCappuccino]

Another interesting option, maybe expose reasoning_effort as a Jinja templating variable? Could be used in Qwen3 where low could fill the <think> block ahead of time, and be OpenAI compatible.