map or grep in scalar context return the number of elements. Scalar assignment enforces scalar context. Use parentheses for list context:

my ($result2) = map { $array[$_][0] =~ /goat/ ? $_ : () } 0..$#array;
my ($result3) = grep { $array[$_][0] =~ /goat/ } 0..$#array;
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or subscript the resulting list:

my $result2 = (map { $array[$_][0] =~ /goat/ ? $_ : () } 0..$#array)[0
+];
my $result3 = (grep { $array[$_][0] =~ /goat/ } 0..$#array)[0];
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