The "New World" is neither confirmed nor denied to be (an alternate dimension version of) Earth, but there are plenty of implications that Shiver Star is, such as the continental land mass shapes and moon.
Some of the Splatoon devs have commented on this sort of thing, saying that it's actually common for Nintendo games to have a bright and colorful exterior that hides a "hidden darkness."
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KYMweatherly23
Jan 04, 2023 at 11:35AM EST in reply to
Mistress Fortune
Jan 04, 2023 at 12:38PM EST