Everything you need to escape from this closet is in here with you. You begin the game with your spider amulet, which is important, but totem magic requires both an amulet and an eyestone. Inspect your surroundings carefully. Leave no stone, so to speak, unturned.
Hint 1
Look in the plastic lost and found crate.
Hint 2
Take the bat amulet, but then take the olivine eyestone out of it. Check out the olivine eyestone.
Hint 3
Put the olivine eyestone in the spider amulet. Make sure you're wearing the spider amulet.
Hint 4
Talk to the spider.
Hint 5
By now you've probably already tried smashing through the wall with your bare fists. But Charybdis isn't buff enough for that kind of action. Maybe talk to the spider again.
Hint 6
What in this room is heavy enough to bust through a wall?
Hint 7
Throw the safe at the wall.
Hint 8
Enter the hole in the wall.
Once you're out of that closet, you're free to roam around the town of Skuga Lake. There's lots of stuff to discover, and no set order in which to accomplish anything, so feel free to explore on your own for a while.
But if you do get stuck, you can continue to the next part of the guide.