As I said, I have not tried to use a proper coil lifter tool yet on that model of engine, but, looking again at the picture in your opening posting, you will see what I meant about there being a cable management tray in there, so what I found that I neded to do, even when using two screwdrivers was, open up the clips on the cable tray and start to remove the coils, it will be the same way with a tool, there should be enough room to clip the tool on and start at one end and ease them all up - you will need to do that as you will run out of cabling if you try to just remove one at a time, doing it my way avoids needing to unplug a single coil - if I remember correctly!
Disconnecting these VAG type of connectors is not rocket science, but it needs a bit of care and understanding to get every one apart with no damage - to the extent that I have a large empty VAG type connector that I keep purely for rechecking exactly
how to open the latch, it is done by inserting a suitable flat blade screwdriver into the small opening on the
top of the connector
after pressing the mating connector pair together to remove any load from that latch, then ease the connector pair apart. So, never be tempted to stick a screwdriver into the small opening on the
end of the connector as that only forces the latch further down and not up!
Edit:- looking at that picture again, the latches are on the underside of the connectors as they are placed in the engine - another very good reason to free up the cable restraints prior to easing up these coils!