feat: Add health check endpoint

Introduce a new health check endpoint at `/api/health`. This endpoint
returns a JSON response indicating the server's status and configuration
details, such as the port, data path, and configured URLs for external
services.

This change also refactors the application setup by:
- Creating a `lib.rs` file to house the `create_router` function, making
  it
  reusable for both the main application and integration tests.
- Moving configuration loading logic into `main.rs` and passing it as a
  shared state (`Arc<Config>`) to the router.
- Adding a unit test (`health_test.rs`) to verify the functionality of
  the
  health check endpoint.
- Updating `Cargo.toml` and `Cargo.lock` to include the `tower`
  dependency,
  which is used for testing.

server/tests/health_test.rs

@@ -0,0 +1,73 @@
+use std::collections::HashMap;
+use std::sync::Arc;
+
+use axum::body::Body;
+use axum::http::{Request, StatusCode};
+use tower::util::ServiceExt;
+
+use doctate_server::config::Config;
+
+fn test_config() -> Arc<Config> {
+    Arc::new(Config {
+        server_port: 3000,
+        data_path: "/tmp/doctate-test".into(),
+        log_level: "info".into(),
+        log_path: "/tmp/doctate-test/logs".into(),
+        log_max_days: 90,
+        users: vec![],
+        api_keys: HashMap::new(),
+        retention_audio_days: 30,
+        retention_transcript_days: 30,
+        retention_document_days: 0,
+        whisper_url: "http://localhost:10300".into(),
+        whisper_timeout_seconds: 120,
+        ollama_url: "http://localhost:11434".into(),
+        ollama_model: "gemma3:4b".into(),
+        ollama_keep_alive: 0,
+        llm_url: String::new(),
+        llm_api_key: String::new(),
+        llm_model: String::new(),
+        llm_temperature: 0.0,
+        session_timeout_hours: 8,
+    })
+}
+
+#[tokio::test]
+async fn health_returns_ok() {
+    let app = doctate_server::create_router(test_config());
+
+    let response = app
+        .oneshot(
+            Request::builder()
+                .uri("/api/health")
+                .body(Body::empty())
+                .unwrap(),
+        )
+        .await
+        .unwrap();
+
+    assert_eq!(response.status(), StatusCode::OK);
+}
+
+#[tokio::test]
+async fn health_returns_json_with_status() {
+    let app = doctate_server::create_router(test_config());
+
+    let response = app
+        .oneshot(
+            Request::builder()
+                .uri("/api/health")
+                .body(Body::empty())
+                .unwrap(),
+        )
+        .await
+        .unwrap();
+
+    let body = axum::body::to_bytes(response.into_body(), usize::MAX)
+        .await
+        .unwrap();
+    let json: serde_json::Value = serde_json::from_slice(&body).unwrap();
+
+    assert_eq!(json["status"], "ok");
+    assert_eq!(json["port"], 3000);
+}