[General Questions and Answers] AllesMeins:
So to just give you a "kind of solution" if somebody stumbles upon this. I solved this by (very crudely) copying together my own app that's always active and waits for "screen on" to re-enable wifi. That can be done without root on my device

MainActivity.java

import android.content.Intent;
import android.os.Bundle;
import android.support.v4.content.ContextCompat;
import android.support.v7.app.AppCompatActivity;
import android.view.View;
import android.widget.Button;
public class MainActivity extends AppCompatActivity {
Button btnStartService, btnStopService;
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main_activity);
btnStartService = findViewById(R.id.buttonStartService);
btnStopService = findViewById(R.id.buttonStopService);
btnStartService.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
startService();
}
});
btnStopService.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
stopService();
}
});
}
public void startService() {
Intent serviceIntent = new Intent(this, ForegroundService.class);
serviceIntent.putExtra("inputExtra", "Monitoring WifiStatus");

Intent onOffIntend = new Intent(this, OnOffReceiver.class);
startService(onOffIntend);

ContextCompat.startForegroundService(this, serviceIntent);
}
public void stopService() {
Intent serviceIntent = new Intent(this, ForegroundService.class);
stopService(serviceIntent);

Intent onOffIntend = new Intent(this, OnOffReceiver.class);
stopService(onOffIntend);
}
}

OnOffReciever.java:

import android.app.Service;
import android.content.BroadcastReceiver;
import android.content.Context;
import android.content.Intent;
import android.content.IntentFilter;
import android.net.wifi.WifiManager;
import android.os.IBinder;
import android.util.Log;

public class OnOffReceiver extends Service {

@Override
public IBinder onBind(Intent arg0) {
// TODO Auto-generated method stub
return null;
}

@Override
public int onStartCommand(Intent intent, int flags, int startId) {
registerReceiver(new BroadcastReceiver() {

public void onReceive(Context context, Intent intent) {
//This happens when the screen is switched off
Log.w("WifiWakeUp","Screen Off");
}
}, new IntentFilter(Intent.ACTION_SCREEN_OFF));

registerReceiver(new BroadcastReceiver() {

public void onReceive(Context context, Intent intent) {
//This happens when the screen is turned on and screen lock deactivated
Log.w("WifiWakeUp","Screen On");
WifiManager wifi = (WifiManager) getSystemService(Context.WIFI_SERVICE);
wifi.setWifiEnabled(true);
}
}, new IntentFilter(Intent.ACTION_USER_PRESENT));

return START_STICKY;
}

@Override
public void onDestroy() {
super.onDestroy();
}

}

Foregroundservice.java

import android.app.Notification;
import android.app.NotificationChannel;
import android.app.NotificationManager;
import android.app.PendingIntent;
import android.app.Service;
import android.content.Intent;
import android.os.Build;
import android.os.IBinder;
import android.support.annotation.Nullable;
import android.support.v4.app.NotificationCompat;

public class ForegroundService extends Service {
public static final String CHANNEL_ID = "ForegroundServiceChannel";
@Override
public void onCreate() {
super.onCreate();
}
@Override
public int onStartCommand(Intent intent, int flags, int startId) {
String input = intent.getStringExtra("inputExtra");
createNotificationChannel();
Intent notificationIntent = new Intent(this, MainActivity.class);
PendingIntent pendingIntent = PendingIntent.getActivity(this,
0, notificationIntent, 0);
Notification notification = new NotificationCompat.Builder(this, CHANNEL_ID)
.setContentTitle("WifiWakeUp")
.setContentText(input)
.setSmallIcon(R.drawable.ic_baseline_wifi_24)
.setContentIntent(pendingIntent)
.build();
startForeground(1, notification);
//do heavy work on a background thread
//stopSelf();
return START_NOT_STICKY;
}
@Override
public void onDestroy() {
super.onDestroy();
}
@Nullable
@Override
public IBinder onBind(Intent intent) {
return null;
}

private void createNotificationChannel() {
if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
NotificationChannel serviceChannel = new NotificationChannel(
CHANNEL_ID,
"Foreground Service Channel",
NotificationManager.IMPORTANCE_DEFAULT
);
NotificationManager manager = getSystemService(NotificationManager.class);
manager.createNotificationChannel(serviceChannel);
}
}

}