feat(user): add email check endpoint for registered user detection

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

backend/handlers/user/guest.go

@@ -1,7 +1,9 @@
 package user
 
 import (
+	"database/sql"
 	"encoding/json"
+	"errors"
 	"log"
 	"net/http"
 	"net/mail"
@@ -126,3 +128,60 @@ func CreateGuestUserHandler(w http.ResponseWriter, r *http.Request) {
 	w.WriteHeader(http.StatusCreated)
 	json.NewEncoder(w).Encode(CreateGuestUserResponse{ID: userID, Role: "guest"})
 }
+
+// GET /api/check-email?email=...&firstName=...&lastName=...&phone=...
+// Returns { suggestion: "login" | "check" | null } based on whether the email
+// belongs to a registered user and how closely the provided details match.
+// Relies on nginx restricting access to frontend-only traffic.
+func CheckEmailHandler(w http.ResponseWriter, r *http.Request) {
+	email := strings.ToLower(strings.TrimSpace(r.URL.Query().Get("email")))
+	if email == "" {
+		http.Error(w, "email query parameter required", http.StatusBadRequest)
+		return
+	}
+
+	if _, err := mail.ParseAddress(email); err != nil {
+		http.Error(w, "invalid email format", http.StatusBadRequest)
+		return
+	}
+
+	firstName := strings.TrimSpace(r.URL.Query().Get("firstName"))
+	lastName := strings.TrimSpace(r.URL.Query().Get("lastName"))
+	phone := strings.TrimSpace(r.URL.Query().Get("phone"))
+
+	var dbFirstName, dbLastName, dbPhone *string
+	err := db.DB.QueryRow(r.Context(), `
+		SELECT n_first_name, n_last_name, phone
+		FROM users
+		WHERE email = $1 AND account_role != 'guest'
+	`, email).Scan(&dbFirstName, &dbLastName, &dbPhone)
+
+	var suggestion *string
+	if err == nil {
+		matchesNames := firstName != "" && lastName != "" &&
+			dbFirstName != nil && dbLastName != nil &&
+			strings.EqualFold(firstName, *dbFirstName) &&
+			strings.EqualFold(lastName, *dbLastName)
+
+		matchesPhone := phone != "" &&
+			dbPhone != nil &&
+			phone == *dbPhone
+
+		if matchesNames && matchesPhone {
+			s := "login"
+			suggestion = &s
+		} else {
+			s := "check"
+			suggestion = &s
+		}
+	} else if !errors.Is(err, sql.ErrNoRows) {
+		log.Printf("Failed to check email: %v", err)
+		http.Error(w, "database error", http.StatusInternalServerError)
+		return
+	}
+
+	w.Header().Set("Content-Type", "application/json")
+	json.NewEncoder(w).Encode(map[string]interface{}{
+		"suggestion": suggestion,
+	})
+}