feat(api): add health probes, OpenAPI doc, and router

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

crates/api/src/health.rs

@@ -0,0 +1,62 @@
+use axum::{Json, Router, extract::State, http::StatusCode, response::IntoResponse, routing::get};
+use serde::Serialize;
+use utoipa::ToSchema;
+
+use crate::AppState;
+
+/// Liveness payload: the process is running.
+#[derive(Serialize, ToSchema)]
+pub(crate) struct Live {
+    /// Always `"ok"` when the process serves requests.
+    pub status: &'static str,
+}
+
+/// Readiness payload: dependencies were checked.
+#[derive(Serialize, ToSchema)]
+pub(crate) struct Ready {
+    /// `"ok"` when ready, `"degraded"` otherwise.
+    pub status: &'static str,
+    /// Whether the database responded to a ping.
+    pub database: bool,
+}
+
+/// Liveness probe — no dependencies checked.
+#[utoipa::path(get, path = "/health/live", responses((status = 200, body = Live)))]
+pub(crate) async fn live() -> Json<Live> {
+    Json(Live { status: "ok" })
+}
+
+/// Readiness probe — confirms the database answers.
+#[utoipa::path(
+    get,
+    path = "/health/ready",
+    responses(
+        (status = 200, body = Ready, description = "Ready"),
+        (status = 503, body = Ready, description = "A dependency is unavailable")
+    )
+)]
+pub(crate) async fn ready(State(state): State<AppState>) -> impl IntoResponse {
+    match state.db.ping().await {
+        Ok(()) => (
+            StatusCode::OK,
+            Json(Ready {
+                status: "ok",
+                database: true,
+            }),
+        ),
+        Err(_) => (
+            StatusCode::SERVICE_UNAVAILABLE,
+            Json(Ready {
+                status: "degraded",
+                database: false,
+            }),
+        ),
+    }
+}
+
+/// Health routes, parameterized over [`AppState`].
+pub(crate) fn routes() -> Router<AppState> {
+    Router::new()
+        .route("/health/live", get(live))
+        .route("/health/ready", get(ready))
+}