Only $, @, \ and the end delimiter (" in this case) need to escaped in double-quoted strings.
my $url = "https://colomanager\.\/stats\/cgi\?sid\=1242418655166\&area=recent\&action=frame\&width=1135\&id=576697218059\&";
can be written more readably as
my $url = "https://colomanager./stats/cgi?sid=1242418655166&area=recent&action=frame&width=1135&id=576697218059&";