2 Core with one ethernet module - arduino

Question

I am using raspberry pi pico with earle's pico core earlepicocore. I am using W5500 with them and I am using this library for it khoih-prog/EthernetWebServer . I hava a lot of code like 1000+ line. I am doing http get and post request and then doing some stuff with these datas. I initialize W5500 ethernet on core 0. Here is my code ;
void setup()
{
uint16_t index = millis() % NUMBER_OF_MAC;
Ethernet.begin(mac[index], 1000);
}
void loop()
{
Serial.println("making GET request");
int statusCode = httpClient.responseStatusCode();
String response = httpClient.responseBody();
.
.
.
}
void setup1()
{
}
void loop1()
{
Serial.println("making GET request");
int statusCode = httpClient.responseStatusCode();
String response = httpClient.responseBody();
.
.
.
}
As I said, I can only use ethernet to activate in 1 core. When I activate it in 2 cores, an error occurs.
uint16_t index = millis() % NUMBER_OF_MAC;
Ethernet.begin(mac[index], 1000);
When I start the code, void loop1 can http request too but after a bit, W5500 give code -2 and -3. Errors :
// Could not connect to the server
static const int HTTP_ERROR_CONNECTION_FAILED = -1;
// This call was made when the EthernetHttpClient class wasn't expecting it
// to be called. Usually indicates your code is using the class
// incorrectly
static const int HTTP_ERROR_API = -2;
// Spent too long waiting for a reply
static const int HTTP_ERROR_TIMED_OUT = -3;
// The response from the server is invalid, is it definitely an HTTP
// server?
static const int HTTP_ERROR_INVALID_RESPONSE = -4;
So my question is, is this error appears because I am using ethernet on core 1 without initialize it ?
Thank you.