Ok after doing so did you restart steam? On your library list Fallout 4 you will see right under Achievements a box called DLC, you should see item/install/Acquired with the Fallout 4 Automatron installed a check box to make it active then the date it was purchased/gotten, under that you will see greyed out Fallout 4 Season Pass Not Installed a check mark should be active then the date of purchase/registered.
If nothing is showing up even after a reboot of steam, try entering your Season Pass key again, if it says the key is already in use, you may have to contact valve support. But double check in your inventory under your name to make sure that steam didn't toss it into that to use for later or give away. Never had that happen but its the only things I can think of. If you do have those things enabled in the DLC all mods/DLC are now activated in the games own game menu it should have auto enabled. But you can check in the main menu. Also the Season Pass has its own code, look in all of your stuff from gamestop. There is no Fallout 4 key with the season pass included in the same code. You should have a second code.