fix(auth): 为登录链路增加有界超时

为 PostgreSQL 连接、就绪检查和本地登录设置分层超时，数据库不可用时返回稳定 503 错误码并记录无凭据的连接池统计。

前端登录在 10 秒后取消请求并兼容调用方 AbortSignal，Nginx 登录精确路由限制上游为 15 秒，同时更新 OpenAPI 和回归测试。

apps/api/internal/store/postgres.go

@@ -7,6 +7,7 @@ import (
 	"encoding/base64"
 	"encoding/json"
 	"errors"
+	"net"
 	"strings"
 	"time"
 	"unicode"
@@ -22,6 +23,11 @@ type Store struct {
 	pool *pgxpool.Pool
 }
 
+const (
+	postgresApplicationName = "easyai-ai-gateway"
+	postgresConnectTimeout  = 5 * time.Second
+)
+
 func defaultAPIKeyScopes() []string {
 	return []string{"chat", "embedding", "rerank", "image", "video", "music", "audio", "voice_clone"}
 }
@@ -67,7 +73,11 @@ var (
 )
 
 func Connect(ctx context.Context, databaseURL string) (*Store, error) {
-	pool, err := pgxpool.New(ctx, databaseURL)
+	config, err := postgresPoolConfig(databaseURL)
+	if err != nil {
+		return nil, err
+	}
+	pool, err := pgxpool.NewWithConfig(ctx, config)
 	if err != nil {
 		return nil, err
 	}
@@ -78,6 +88,38 @@ func Connect(ctx context.Context, databaseURL string) (*Store, error) {
 	return &Store{pool: pool}, nil
 }
 
+func postgresPoolConfig(databaseURL string) (*pgxpool.Config, error) {
+	config, err := pgxpool.ParseConfig(databaseURL)
+	if err != nil {
+		return nil, err
+	}
+	config.ConnConfig.ConnectTimeout = postgresConnectTimeout
+	config.ConnConfig.RuntimeParams["application_name"] = postgresApplicationName
+	return config, nil
+}
+
+func IsPostgresUnavailable(err error) bool {
+	if err == nil {
+		return false
+	}
+	if errors.Is(err, context.DeadlineExceeded) {
+		return true
+	}
+	var connectError *pgconn.ConnectError
+	if errors.As(err, &connectError) {
+		return true
+	}
+	var networkError net.Error
+	if errors.As(err, &networkError) {
+		return true
+	}
+	var postgresError *pgconn.PgError
+	if errors.As(err, &postgresError) {
+		return strings.HasPrefix(postgresError.Code, "08") || postgresError.Code == "53300" || strings.HasPrefix(postgresError.Code, "57P0")
+	}
+	return pgconn.SafeToRetry(err)
+}
+
 func (s *Store) Close() {
 	s.pool.Close()
 }