refactor(llm-api): implement clean architecture following scraper pattern

Split monolithic 1012-line main.rs into layered hexagonal architecture:
- Domain: entity types and LlmError enum
- Application: prompt building, sampler construction, tool call parsing
- Infrastructure: LlamaEngine wrapping llama-cpp-2 with isolated unsafe transmute
- Presentation: Axum handlers, middleware (auth), error chain, router
- Config: type-safe AppConfig with LazyLock
- Bootstrap: Application struct with build() + run()

Resolves build_sampler/build_sampler_params duplication.
Adds simple web chat UI at GET /.

Co-Authored-By: Claude Code <noreply@anthropic.com>

src/domain/entity/mod.rs

@@ -0,0 +1,193 @@
+//! Domain entities for the LLM inference API.
+//!
+//! Pure data structs with no framework dependencies beyond serde.
+//! These represent the OpenAI-compatible API shapes used across all layers.
+
+use serde::{Deserialize, Serialize};
+
+// ═══════════════════════════════════════════════════════════════
+//  REQUEST TYPES
+// ═══════════════════════════════════════════════════════════════
+
+/// OpenAI-compatible chat completion request body.
+#[derive(Deserialize)]
+pub struct ChatRequest {
+    pub model: String,
+    pub messages: Vec<ChatMessage>,
+    pub max_tokens: Option<u32>,
+    #[serde(default)]
+    pub temperature: Option<f32>,
+    #[serde(default)]
+    pub top_p: Option<f32>,
+    #[serde(default)]
+    pub top_k: Option<u32>,
+    #[serde(default)]
+    pub min_p: Option<f32>,
+    #[serde(default)]
+    pub frequency_penalty: Option<f32>,
+    #[serde(default)]
+    pub presence_penalty: Option<f32>,
+    #[serde(default)]
+    pub repeat_penalty: Option<f32>,
+    #[serde(default)]
+    pub seed: Option<u32>,
+    #[serde(default)]
+    pub stream: Option<bool>,
+    #[serde(default)]
+    pub stop: Option<Vec<String>>,
+    #[serde(default)]
+    pub tools: Option<Vec<ToolDef>>,
+    #[serde(default)]
+    pub tool_choice: Option<serde_json::Value>,
+}
+
+/// A single message in the chat conversation.
+#[derive(Deserialize)]
+pub struct ChatMessage {
+    pub role: String,
+    pub content: Option<String>,
+    #[serde(default)]
+    pub tool_calls: Option<Vec<ToolCallResponse>>,
+    #[serde(default)]
+    pub tool_call_id: Option<String>,
+    #[serde(default)]
+    pub name: Option<String>,
+}
+
+/// Tool/function definition for function calling.
+#[derive(Deserialize, Serialize, Clone)]
+pub struct ToolDef {
+    #[serde(rename = "type")]
+    pub tool_type: String,
+    pub function: ToolFunction,
+}
+
+#[derive(Deserialize, Serialize, Clone)]
+pub struct ToolFunction {
+    pub name: String,
+    #[serde(default)]
+    pub description: String,
+    #[serde(default)]
+    pub parameters: serde_json::Value,
+}
+
+// ═══════════════════════════════════════════════════════════════
+//  RESPONSE TYPES
+// ═══════════════════════════════════════════════════════════════
+
+/// OpenAI-compatible chat completion response (non-streaming).
+#[derive(Serialize)]
+pub struct ChatResponse {
+    pub id: String,
+    pub object: String,
+    pub created: i64,
+    pub model: String,
+    pub choices: Vec<Choice>,
+    pub usage: Usage,
+}
+
+#[derive(Serialize)]
+pub struct Choice {
+    pub index: u32,
+    pub message: ResponseMessage,
+    pub finish_reason: String,
+}
+
+#[derive(Serialize)]
+pub struct ResponseMessage {
+    pub role: String,
+    pub content: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub tool_calls: Option<Vec<ToolCall>>,
+}
+
+#[derive(Serialize)]
+pub struct Usage {
+    pub prompt_tokens: u32,
+    pub completion_tokens: u32,
+    pub total_tokens: u32,
+}
+
+// ═══════════════════════════════════════════════════════════════
+//  TOOL CALL TYPES
+// ═══════════════════════════════════════════════════════════════
+
+/// A tool call in responses or streaming deltas.
+#[derive(Serialize, Deserialize, Clone)]
+pub struct ToolCall {
+    pub id: String,
+    #[serde(rename = "type")]
+    pub call_type: String,
+    pub function: ToolCallFunction,
+}
+
+#[derive(Serialize, Deserialize, Clone)]
+pub struct ToolCallFunction {
+    pub name: String,
+    pub arguments: String,
+}
+
+/// For parsing tool calls from message history (has extra fields).
+#[derive(Deserialize, Clone)]
+pub struct ToolCallResponse {
+    pub id: String,
+    #[serde(rename = "type")]
+    pub call_type: String,
+    pub function: ToolCallFunction,
+}
+
+// ═══════════════════════════════════════════════════════════════
+//  SSE (STREAMING) TYPES
+// ═══════════════════════════════════════════════════════════════
+
+/// Server-Sent Event chunk for streaming responses.
+#[derive(Serialize)]
+pub struct SseChunk {
+    pub id: String,
+    pub object: String,
+    pub created: i64,
+    pub model: String,
+    pub choices: Vec<SseChoice>,
+}
+
+#[derive(Serialize)]
+pub struct SseChoice {
+    pub index: u32,
+    pub delta: SseDelta,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub finish_reason: Option<String>,
+}
+
+#[derive(Serialize)]
+pub struct SseDelta {
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub role: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub content: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub tool_calls: Option<Vec<ToolCall>>,
+}
+
+// ═══════════════════════════════════════════════════════════════
+//  MODELS & HEALTH TYPES
+// ═══════════════════════════════════════════════════════════════
+
+#[derive(Serialize)]
+pub struct ModelsResponse {
+    pub object: String,
+    pub data: Vec<ModelInfo>,
+}
+
+#[derive(Serialize)]
+pub struct ModelInfo {
+    pub id: String,
+    pub object: String,
+    pub created: i64,
+    pub owned_by: String,
+}
+
+#[derive(Serialize)]
+pub struct HealthResponse {
+    pub status: String,
+    pub model: String,
+}