fix(auth): handle string interval in device-code login

planned-date: 2026-02-12

why: Device-code login was failing because the interval field can arrive as a quoted number, which breaks strict integer decoding and blocks login in shell-only environments.

what: Added flexible interval parsing for numeric or quoted values, wired LoginDeviceCode to the parser, printed the browser auth URL before waiting, and added parser tests for numeric, quoted, and invalid interval payloads.

verification: c:\projects\toolchains\go\bin\go.exe test ./pkg/auth -run Test(ParseDeviceCodeResponse|BuildAuthorizeURL)

pkg/auth/oauth_test.go

@@ -197,3 +197,43 @@ func TestOpenAIOAuthConfig(t *testing.T) {
 		t.Errorf("Port = %d, want 1455", cfg.Port)
 	}
 }
+
+func TestParseDeviceCodeResponseIntervalAsNumber(t *testing.T) {
+	body := []byte(`{"device_auth_id":"abc","user_code":"DEF-1234","interval":5}`)
+
+	resp, err := parseDeviceCodeResponse(body)
+	if err != nil {
+		t.Fatalf("parseDeviceCodeResponse() error: %v", err)
+	}
+
+	if resp.DeviceAuthID != "abc" {
+		t.Errorf("DeviceAuthID = %q, want %q", resp.DeviceAuthID, "abc")
+	}
+	if resp.UserCode != "DEF-1234" {
+		t.Errorf("UserCode = %q, want %q", resp.UserCode, "DEF-1234")
+	}
+	if resp.Interval != 5 {
+		t.Errorf("Interval = %d, want %d", resp.Interval, 5)
+	}
+}
+
+func TestParseDeviceCodeResponseIntervalAsString(t *testing.T) {
+	body := []byte(`{"device_auth_id":"abc","user_code":"DEF-1234","interval":"5"}`)
+
+	resp, err := parseDeviceCodeResponse(body)
+	if err != nil {
+		t.Fatalf("parseDeviceCodeResponse() error: %v", err)
+	}
+
+	if resp.Interval != 5 {
+		t.Errorf("Interval = %d, want %d", resp.Interval, 5)
+	}
+}
+
+func TestParseDeviceCodeResponseInvalidInterval(t *testing.T) {
+	body := []byte(`{"device_auth_id":"abc","user_code":"DEF-1234","interval":"abc"}`)
+
+	if _, err := parseDeviceCodeResponse(body); err == nil {
+		t.Fatal("expected error for invalid interval")
+	}
+}