To the OP's comment about the issue with starting the playlist from the beginning rather than shuffle play -
You can do this with AutoInput, since as you mention - just pressing 'Play' with AutoInput rarely starts the playlist from the beginning, instead playing whatever song was last played, and you can easily click "Shuffle" but to start the playlist from the beginning -
Try using AutoInput > Click > Type:List > Value:3
And if 3 doesn't work, try other values. ALSO, the new AutoNotification beta can press any button on any 'widget' type notification in the status bar, even with the screen OFF or LOCKED!
What this means is that - when Spotify is running with it's little widgety thing in the status bar, you can pull all that data into Tasker, and also use Tasker to press Play/Pause, Skip Forward/back, anything that can be pressed in the status bar can now be pressed with Tasker (whereas before it had to be a standard-type notification button). To access this get the AN beta, then run the AN Query, and specify Spotify and all the button ID's will come back in a new array field named %aninternalactions() so to skip forward you'd use AN>Action %aninternalactions(5). It may differ based on device so sometimes you got to experiment with the element number in the array until you get the button action you want.