Serial monitor how can I see it via a wireless network?

I would like to debug / monitor my project with a wireless connection so I don't have to keep the project near my computer. It will be on the same home network. I am using IDE 2.3.4 with ESP8266.

you could use telnet, try a web search for ESP32 telnet

I haven't tried Telnet, but if these are your messages for debugging the code, you can also do it via UDP. It's very easy to implement on the ESP8266. And on the computer you can read them with any free program. I use Packet Sender on Mac. It´s also to Windows Packet Sender - Download.

Additionally, both from the ESP8266 and the computer, you can send packets via Broadcast. This way, during debugging, you won't have reception issues even if the IPs are assigned via DHCP and might change.

I absolutely endorse the UDP solution. In the original code, where it does serial prints sending an UDP packet (to broadcast, to make things easier) is the simplest solution.

If I go the UDP way is there a way to keep all my serial.print lines the same? Also can it work for both serial and Wifi connections?

You can have both at the same time without any problem.

Just duplicate the Serial.print() lines with the UDP sends, or, better, define a function to send to both (I assume you have a function for string sending via UDP broadcast packet).
Like:

  Serial.println("Hello");
  UdpSendString("Hello");

or by mixing the two in a single function like "SendString":

...
void SendString(const char *message) {
  Serial.println(message);
  UdpSendString(messge);
}
...
  SendString("Hello");