Brain-Flak, 68 bytes

({({({})({}[()])}{}<>)<>})<>({<(({}){}<>[({})])>(){[()](<{}>)}{}<>})

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Brain-Flak, 68 bytes

({({({})({}[()])}{}<>)<>})<>({<(({}){}<>[({})])>(){[()](<{}>)}{}<>})

Try it online!

Uses the observation in user202729's answer.

 { } for each input number
 {({})({}[()])}{} compute the square
 ( <>)<> push onto second stack
( ) push sum of squares onto first stack
 <> move to second stack
 { } for each square
 (({}){}<>[({})]) compute 2 * this square - sum of squares
 < >(){[()](<{}>)}{}<> evaluate loop iteration as 1 iff equal
( ) push 1 if any squares matched, 0 otherwise