There seems to be a difference in how events are handled when you preview them directly and when you transition between them, need to investigate that further.
That difference is causing your first attempt with a not playing condition to fail, because while it works when you preview the layout directly, as you would expect, because the Play action comes before the check... when you enter from another layout the condition is hit once, before the timeline starts playing, starting the whole process to exit the layout before the timeline is finished.
Your second attempt, avoids that problem by using the On Finished condition, but the fade to black transition does not work, because the trigger is only hit once, so updating the opacity based on a delta, doesn't work.
In order for that to work, you would need to set a flag on the On Finished trigger, and then based on that flag decide when to start playing your fade to black animation, elsewhere in the event sheet.
You could also add the instance that is the black background to Layout 2, set it to opacity 0% in the editor, and animate it in the same timeline you are using to move the cat. Below an example file showing that method. The good thing is you can get rid of some of the events, as the timeline takes care of everything regarding the animation.
https://www.dropbox.com/s/g714jdw9z3iwzg2/FrankieGame2.zip?dl=0
Your game reminds me of an old DOS game, Alley Cat https://www.youtube.com/watch?v=uZDG4dlU5uY