refactor: centralize CoT parsing in backend for streaming mode (#16394)

* refactor: unify reasoning handling via backend reasoning_content, drop frontend tag parsing

- Updated the chat message component to surface backend-supplied reasoning via message.thinking while showing the raw assistant content without inline tag scrubbing
- Simplified chat streaming to append content chunks directly, stream reasoning into the message model, and persist any partial reasoning when generation stops
- Refactored the chat service SSE handler to rely on server-provided reasoning_content, removing legacy <think> parsing logic
- Refreshed Storybook data and streaming flows to populate the thinking field explicitly for static and streaming assistant messages

* refactor: implement streaming-aware universal reasoning parser

Remove the streaming mode limitation from --reasoning-format by refactoring
try_parse_reasoning() to handle incremental parsing of <think> tags across
all formats.

- Rework try_parse_reasoning() to track whitespace, partial tags, and
  multiple reasoning segments, allowing proper separation of reasoning_content
  and content in streaming mode
- Parse reasoning tags before tool call handling in content-only and Llama 3.x
  formats to ensure inline <think> blocks are captured correctly
- Change default reasoning_format from 'auto' to 'deepseek' for consistent
  behavior
- Add 'deepseek-legacy' option to preserve old inline behavior when needed
- Update CLI help and documentation to reflect streaming support
- Add parser tests for inline <think>...</think> segments

The parser now continues processing content after </think> closes instead of
stopping, enabling proper message.reasoning_content and message.content
separation in both streaming and non-streaming modes.

Fixes the issue where streaming responses would dump everything (including
post-thinking content) into reasoning_content while leaving content empty.

* refactor: address review feedback from allozaur

- Passed the assistant message content directly to ChatMessageAssistant to drop the redundant derived state in the chat message component
- Simplified chat streaming updates by removing unused partial-thinking handling and persisting partial responses straight from currentResponse
- Refreshed the ChatMessage stories to cover standard and reasoning scenarios without the old THINK-tag parsing examples

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* refactor: restore forced reasoning prefix to pass test-chat ([chat] All tests passed)

- store the exact sequence seen on input when 'thinking_forced_open' enforces a reasoning block
- inject this prefix before the first accumulated segment in 'reasoning_content', then clear it to avoid duplication
- repeat the capture on every new 'start_think' detection to properly handle partial/streaming flows

* refactor: address review feedback from ngxson

* debug: say goodbye to curl -N, hello one-click raw stream

- adds a new checkbox in the WebUI to display raw LLM output without backend parsing or frontend Markdown rendering

* Update tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessage.svelte

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* webui: add Storybook example for raw LLM output and scope reasoning format toggle per story

- Added a Storybook example that showcases the chat message component in raw LLM output mode with the provided trace sample
- Updated every ChatMessage story to toggle the disableReasoningFormat setting so the raw-output rendering remains scoped to its own example

* npm run format

* chat-parser: address review feedback from ngxson

Co-authored-by: Xuan Son Nguyen <thichthat@gmail.com>

---------

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>
Co-authored-by: Xuan Son Nguyen <thichthat@gmail.com>

tests/test-chat-parser.cpp

@@ -106,6 +106,34 @@ static void test_reasoning() {
     assert_equals("<think>Cogito</think>", builder.result().content);
     assert_equals("Ergo sum", builder.consume_rest());
   }
+  {
+    const std::string variant("content_only_inline_think");
+    common_chat_syntax syntax = {
+        /* .format = */ COMMON_CHAT_FORMAT_CONTENT_ONLY,
+        /* .reasoning_format = */ COMMON_REASONING_FORMAT_DEEPSEEK,
+        /* .reasoning_in_content = */ false,
+        /* .thinking_forced_open = */ false,
+        /* .parse_tool_calls = */ false,
+    };
+    const std::string input = "<think>Pense</think>Bonjour";
+    auto msg = common_chat_parse(input, false, syntax);
+    assert_equals(variant, std::string("Pense"), msg.reasoning_content);
+    assert_equals(variant, std::string("Bonjour"), msg.content);
+  }
+  {
+    const std::string variant("llama_3_inline_think");
+    common_chat_syntax syntax = {
+        /* .format = */ COMMON_CHAT_FORMAT_LLAMA_3_X,
+        /* .reasoning_format = */ COMMON_REASONING_FORMAT_DEEPSEEK,
+        /* .reasoning_in_content = */ false,
+        /* .thinking_forced_open = */ false,
+        /* .parse_tool_calls = */ false,
+    };
+    const std::string input = "<think>Plan</think>Réponse";
+    auto msg = common_chat_parse(input, false, syntax);
+    assert_equals(variant, std::string("Plan"), msg.reasoning_content);
+    assert_equals(variant, std::string("Réponse"), msg.content);
+  }
   // Test DeepSeek V3.1 parsing - reasoning content followed by "</think>" and then regular content
   {
     common_chat_syntax syntax = {