I try to implement the Thread::Queue module, but the provided example and the other resources I have been reading only consider a defined amount of queued tasks (when this may vary in my case).

What does that mean?

Its unclear what your diagram looks like, but I think Thread::Queue is workable like this

#!/usr/bin/perl --
use strict; use warnings;
use threads stack_size => 4096;
use Thread::Queue;

my %serverQ;
my $resultQ  = Thread::Queue->new;
my @workers  = map {
    my $workQ = Thread::Queue->new;
    threads->create( \&Worker, $workQ, $resultQ );
} 1..10;


...

while( @targets ){
    ...
    if( my $q = $serverQ{ $host } ){
        $q->enqueue( [
        ## 'Foo::bar::deployRoutine', $onearg, $twoarg, $threearg ,
            'deployRoutine' =>
                $targetServer, $deploySource, $deployDest,   "true",
        ] );
    
    ...
    FreeFreeWorkers( \%serverQ ); ## check empty Qs, unassociate from 
+a host
    

...

$_->join for threads->list;
exit( 0 );


sub Worker {
    my( $workQ, $resultQ ) = @_;
    while( defined( my $jobDesc = $workQ->dequeue ) ) {
        my( $package, $function, @args ) = @$jobDesc;
        require Module::Load;
        Module::Load::load( $package );
        $resultQ->enqueue( [ $function->( @args ) ] );
    }
    return;
}
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