Paranoia Agent/WMG

Tsukiko is what happened when Ayumu Kasuga failed to make any friends.

In the universe of Paranoia Agent, Ayumu never entered the plot of Azumanga Daioh. And thus instead of growing up to be Osaka and having some very close friends, she became very lonely and changed her name to Tsukiko Sagi (as sort of a pseudonym for her design career).

Chiyo-chichi was able to appear to both Sakaki and Osaka without ever mentioning him to each other because Osaka has reality warping capabilities that are very weak. In Paranoia Agent, her reality warping powers are so strong that she makes Maromi come to life and makes Shounen Bat a physical entity.

That's why Tsukiko Sagi looks so disturbingly similar to Osaka and the reason why Osaka is such a Nightmare Fuel Station Attendant.

Osaka: And don't you worry. You won't find any dead cats or anything in here, either!

• "Magical" superpowers? Failed to find friends? Associated with the moon and with bad dreams? Surrounded by Ridiculously Cute Critters? That just screams Nightmare Moon.
  • Or Nyarlathotep. (Okay, except for the Ridiculously Cute Critter part.)
    • What would be better for the Crawling Chaos to hide out as than a cute critter? Perhaps he's just feeling ironic this time.

Paranoia Agent takes place in the same world as Candyman

a world where an urban legend can become real if people believe in it hard enough? sounds an awful lot like Candyman to me, just set in Tokyo instead of Chicago