CalloutSampleTest.cls

@IsTest
private class CalloutSampleTest {
    
    public class CalloutMock implements HttpCallout.Service {
        public HttpResponse respond(HttpRequest req) {
            return new HttpResponse();
        }
    }
    
    @IsTest
    static void test() {
        System.runAs([select Id from User where Id = :UserInfo.getUserId()][0]) {
            String name = EncodingUtil.convertToHex(Crypto.generateAesKey(128));
            insert new User(
                LastName = name,
                Username = name + '@example.com',
                Email = name + '@example.com',
                ProfileId = UserInfo.getProfileId(),
                Alias = name.left(8),
                TimeZoneSidKey = 'Asia/Tokyo',
                LocaleSidKey = 'ja_JP',
                EmailEncodingKey = 'UTF-8',
                LanguageLocaleKey = 'ja'
            );
        }
        HttpCallout.setMock(HttpCalloutMock.class, new CalloutMock());
        
        Test.startTest();
        HttpRequest req = new HttpRequest();
        req.setMethod('GET');
        req.setEndpoint('https://login.salesforce.com');
        new HttpCallout().send(req);
        Test.stopTest();
    }

}

HttpCallout.cls

public class HttpCallout {
    
    public interface Service {
        HttpResponse respond(HttpRequest req);
    }
    
    public class ServiceImpl implements Service {
        public HttpResponse respond(HttpRequest req) {
            return new Http().send(req);
        }
    }
    
    private static Service impl {
        get {
            return impl == null ? impl = new ServiceImpl() : impl;
        }
        set;
    }
    
    public HttpResponse send(HttpRequest req) {
        return impl.respond(req);
    }
    
    @TestVisible
    private static void setMock(Service mock) {
        impl = mock;
    }
    
    @TestVisible
    private static void setMock(Type dummy, Service mock) {
        setMock(mock);
    }
    
}

HttpCalloutTest.cls

@IsTest
private class HttpCalloutTest {
    
    public class Mock implements HttpCalloutMock {
        public HttpResponse respond(HttpRequest req) {
            return new HttpResponse();
        }
    }
    
    @IsTest
    static void cover() {
        HttpCallout.setMock(HttpCalloutMock.class, new HttpCallout.ServiceImpl());
        Test.setMock(HttpCalloutMock.class, new Mock());
        new HttpCallout().send(new HttpRequest());
    }

}

new Http().sendをnew HttpCallout().sendに, implements HttpCalloutMockをimplements HttpCallout.Serviceにすれば動くようにしている。