I seems like you can press the left side with any fingers. Doesn't necessarily need to be the thumb.
Once you press the left side of the handle, the door opens and you can just grab the door to fully open it
There's no need to grab the door itself as was shown in the reveal videos (people just didn't know). Once you press the left side, the other side becomes a handle that you can use to open the door.
You can see it done properly here (skip to 1:25)
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