Try setting store_comments before you parse the file:

my $template_tree = HTML::TreeBuilder->new();
$template_tree->->store_comments(1);
$template_tree->parse_file (\*TEMPLATE);
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Note: the HTML::TreeBuilder documentation says:

$root->store_comments(value)

This determines whether TreeBuilder will normally store comments found while parsing content into $root. Currently, this is off by default.