Use the menu letter as the key and defer creation of hash entries until they are needed cleans things up a little. Consider:

use strict;
use warnings;

my %menus;
my @sorted_applications = qw(app1 App2 bapp bopp cap cop);

for my $app (@sorted_applications) {
    # Create and populate menus
    $app = lc $app;
    
    my $letter = substr $app, 0, 1;
    
    if (! exists $menus{$letter}) {
        #create the menu entry
        $menus{$letter}{label} = '$nbsp; ' . uc $letter;
        $menus{$letter}{items} = []; # Not required, but shows intent
    }
    
    push @{$menus{$letter}{items}}, $app;
}

# Dump the menu structure
for my $topMenu (sort keys %menus) {
    print "$menus{$topMenu}{label}\n";
    print "   $_\n" for @{$menus{$topMenu}{items}};
}
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Prints:

$nbsp; A
   app1
   app2
$nbsp; B
   bapp
   bopp
$nbsp; C
   cap
   cop
[download]