docs: Update server README to reflect PR #20297 (#20560)

Author: Tomeamis

tools/server/README.md

@@ -215,7 +215,9 @@ For the full list of features, please refer to [server's changelog](https://gith
 | `--models-autoload, --no-models-autoload` | for router server, whether to automatically load models (default: enabled)<br/>(env: LLAMA_ARG_MODELS_AUTOLOAD) |
 | `--jinja, --no-jinja` | whether to use jinja template engine for chat (default: enabled)<br/>(env: LLAMA_ARG_JINJA) |
 | `--reasoning-format FORMAT` | controls whether thought tags are allowed and/or extracted from the response, and in which format they're returned; one of:<br/>- none: leaves thoughts unparsed in `message.content`<br/>- deepseek: puts thoughts in `message.reasoning_content`<br/>- deepseek-legacy: keeps `<think>` tags in `message.content` while also populating `message.reasoning_content`<br/>(default: auto)<br/>(env: LLAMA_ARG_THINK) |
-| `--reasoning-budget N` | controls the amount of thinking allowed; currently only one of: -1 for unrestricted thinking budget, or 0 to disable thinking (default: -1)<br/>(env: LLAMA_ARG_THINK_BUDGET) |
+| `-rea, --resoning [on\|off\|auto]` | Use reasoning/thinking in the chat ('on', 'off', or 'auto', default: 'auto' (detect from template))<br/>(env: LLAMA_ARG_REASONING) |
+| `--reasoning-budget N` | token budget for thinking: -1 for unrestricted, 0 for immediate end, N>0 for token budget (default: -1)<br/>(env: LLAMA_ARG_THINK_BUDGET) |
+| `--reasoning-budget-message MESSAGE` | message injected before the end-of-thinking tag when reasoning budget is exhausted (default: none)<br/>(env: LLAMA_ARG_THINK_BUDGET_MESSAGE) |
 | `--chat-template JINJA_TEMPLATE` | set custom jinja chat template (default: template taken from model's metadata)<br/>if suffix/prefix are specified, template will be disabled<br/>only commonly used templates are accepted (unless --jinja is set before this flag):<br/>list of built-in templates:<br/>bailing, bailing-think, bailing2, chatglm3, chatglm4, chatml, command-r, deepseek, deepseek2, deepseek3, exaone-moe, exaone3, exaone4, falcon3, gemma, gigachat, glmedge, gpt-oss, granite, grok-2, hunyuan-dense, hunyuan-moe, kimi-k2, llama2, llama2-sys, llama2-sys-bos, llama2-sys-strip, llama3, llama4, megrez, minicpm, mistral-v1, mistral-v3, mistral-v3-tekken, mistral-v7, mistral-v7-tekken, monarch, openchat, orion, pangu-embedded, phi3, phi4, rwkv-world, seed_oss, smolvlm, solar-open, vicuna, vicuna-orca, yandex, zephyr<br/>(env: LLAMA_ARG_CHAT_TEMPLATE) |
 | `--chat-template-file JINJA_TEMPLATE_FILE` | set custom jinja chat template file (default: template taken from model's metadata)<br/>if suffix/prefix are specified, template will be disabled<br/>only commonly used templates are accepted (unless --jinja is set before this flag):<br/>list of built-in templates:<br/>bailing, bailing-think, bailing2, chatglm3, chatglm4, chatml, command-r, deepseek, deepseek2, deepseek3, exaone-moe, exaone3, exaone4, falcon3, gemma, gigachat, glmedge, gpt-oss, granite, grok-2, hunyuan-dense, hunyuan-moe, kimi-k2, llama2, llama2-sys, llama2-sys-bos, llama2-sys-strip, llama3, llama4, megrez, minicpm, mistral-v1, mistral-v3, mistral-v3-tekken, mistral-v7, mistral-v7-tekken, monarch, openchat, orion, pangu-embedded, phi3, phi4, rwkv-world, seed_oss, smolvlm, solar-open, vicuna, vicuna-orca, yandex, zephyr<br/>(env: LLAMA_ARG_CHAT_TEMPLATE_FILE) |
 | `--prefill-assistant, --no-prefill-assistant` | whether to prefill the assistant's response if the last message is an assistant message (default: prefill enabled)<br/>when this flag is set, if the last message is an assistant message then it will be treated as a full message and not prefilled<br/><br/>(env: LLAMA_ARG_PREFILL_ASSISTANT) |