I have legitimately always been confused by the bodega thing for the same reason.
We have several chains that do exactly that and they're just called "corner stores".
"You can get eggs, toilet paper, and Gatorade"
Damn, that's called a Spar, or Premier, or Londis.
This is one of those things that's just unknown and vague enough that it can't be cringe.
If someone asks you what it is you can just say "oh it's a cute bear cos I like them" .