I'm not able to see any System.debug(); calls from my Apex class in my debug logs, which is being called via JavaScript Remoting in a Visualforce page.

Client Portal APEX Controller (@RemoteAction method is the one I'm calling with the debug statement):

public class ClientPortalHomeController {
    public Contact contact {get; private set;}
    
    public ClientPortalHomeController() {
        contact = [
            Select Id, FirstName, LastName, Birthdate
            From Contact
            Where Id In (Select ContactId From User Where Id = :UserInfo.getUserId())
        ];
    }
    
    @RemoteAction
    public static String UserIDLookup(String handle) {
        HttpRequest request = new HttpRequest();
        request.setEndpoint('https://jsonplaceholder.typicode.com/posts/1');
        request.setMethod('GET');

        Http http = new Http();
        HttpResponse response = http.send(request);
        System.debug(LoggingLevel.INFO , response);
        return response.getBody();
    }
    
}

Debug Logs page in Setup:

I even changed the APEX field to Debug as shown in this answer.