Thanks to tobyink for pointing me in the Graph direction I have found a simple solution:

use Graph;

my @AoA = (
    [11,29, 10,25],
    [15,35, 11,29],
    [15,15, 11,21],
    [10,25, 11,21],
    [15,35, 21,39],
    [25,40, 21,39],
    [21,11, 25,10],
    [15,15, 21,11],
    [35,35, 29,39],
    [29,39, 25,40],
    [35,15, 29,11],
    [25,10, 29,11],
    [40,25, 39,29],
    [35,35, 39,29],
    [39,21, 40,25],
    [35,15, 39,21],

    [61,29, 60,25],
    [60,25, 61,21],
);

my $graph = Graph::Undirected->new;

for my $pair (@AoA) {
    my ($x1, $y1, $x2, $y2) = @$pair;
    $graph->add_edge("$x1,$y1", "$x2,$y2");
}
my @lines = $graph->connected_components();
for my $line (@lines) {
    print "@$line\n";
}

# Result

35,15 39,21 40,25 39,29 35,35 29,39 25,40 21,39 15,35 11,29 10,25 11,2
+1 15,15 21,11 25,10 29,11

61,21 60,25 61,29
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