I thought it was a very easy problem... but I haven't solved for quite some time. For now, pressing back button will turn off the app. I want to go back by pressing the back button. Fragment containing the webview. HomeFragment.java
public class HomeFragment extends Fragment {
    WebView webView;
    public HomeFragment() {
        // Required empty public constructor
    }
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        // Inflate the layout for this fragment
        return inflater.inflate(R.layout.fragment_home, container, false);
    }
    @Override
    public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);
        webView = view.findViewById(R.id.home_webview);
        String url = "https://galaxyhub.kr/starcitizen";
        webView.loadUrl(url);
        webView.getSettings().setJavaScriptEnabled(true);
        final ProgressDialog dialog = ProgressDialog.show(getActivity(),"", "Loading", true);
        webView.setWebViewClient(new WebViewClient(){
            @Override
            public void onReceivedError(WebView view, WebResourceRequest request, WebResourceError error) {
                Toast.makeText(getActivity(), "URL ERROR", Toast.LENGTH_SHORT).show();
            }
            @Override
            public void onPageStarted(WebView view, String url, Bitmap favicon) {
                dialog.show();
            }
            @Override
            public void onPageFinished(WebView view, String url) {
                super.onPageFinished(view, url);
                dialog.dismiss();
            }
        });
    }
}
I heard that I should also write in the MainActivity. I'll post it right away if needed.
package com.example.starcitizen.fragment;
import android.app.Activity;
import android.app.ProgressDialog;
import android.graphics.Bitmap;
import android.os.Bundle;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.webkit.WebResourceError;
import android.webkit.WebResourceRequest;
import android.webkit.WebView;
import android.webkit.WebViewClient;
import android.widget.Toast;
import androidx.activity.OnBackPressedCallback;
import androidx.annotation.Nullable;
import androidx.fragment.app.Fragment;
import com.example.starcitizen.R;
/**
 * A simple {@link Fragment} subclass.
 */
public class HomeFragment extends Fragment {
    WebView webView;
    OnBackPressedCallback callback = new OnBackPressedCallback(true) {
        @Override
        public void handleOnBackPressed() {
            if (webView.canGoBack()) {
                webView.goBack();
            } else {
                //use this if you need to call the Activity
                //backpress for default back action
                requireActivity().onBackPressed();
            }
        }
    };
    @Override
    public void onCreate(@Nullable Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        requireActivity().getOnBackPressedDispatcher().addCallback(this, callback);
    }
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        // Inflate the layout for this fragment
        return inflater.inflate(R.layout.fragment_home, container, false);
    }
    @Override
    public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);
        webView = view.findViewById(R.id.home_webview);
        String url = "https://galaxyhub.kr/starcitizen";
        webView.loadUrl(url);
        webView.getSettings().setJavaScriptEnabled(true);
        final ProgressDialog dialog = ProgressDialog.show(getActivity(),"", "Loading",
                true);
        webView.setWebViewClient(new WebViewClient(){
            @Override
            public void onReceivedError(WebView view, WebResourceRequest request, WebResourceError error) {
                Toast.makeText(getActivity(), "URL ERROR", Toast.LENGTH_SHORT).show();
            }
            @Override
            public void onPageStarted(WebView view, String url, Bitmap favicon) {
                dialog.show();
            }
            @Override
            public void onPageFinished(WebView view, String url) {
                super.onPageFinished(view, url);
                dialog.dismiss();
            }
        });
    }
}
Now this code is running!
 
    