Your first code seems to work for me, maybe you have a version/platform problem? I'm using Tk-804.027 on linux.The following code works fine for me, which is similar to your code. Maybe I don't understand your problem.

#!/usr/bin/perl
use strict;
use Tk;
use Tk::BrowseEntry;

my $mw = MainWindow->new;

# Mainwindow: sizex/y, positionx/y
$mw->geometry("200x200+100+120");

my $shortlist = [qw(a b c d)];
my $longlist = [qw(a b c d e f g h i j k l m n o p r s t u w)];
my $reallonglist =[(1..100)];

# Create dropdown and another element which shows my selection
my $dropdown_value = 42;
my $dropdown = $mw->BrowseEntry(
        -label => "Label",
        -choices => [('')],
        -variable => \$dropdown_value,
        -autolimitheight => 1
        )->pack;

$mw->Button( -text => "Short List", -command => sub{ 
        $dropdown->configure(-choices => $shortlist)})->pack;
    
    
$mw->Button( -text => "Long List", -command => sub{ 
        $dropdown->configure(-choices => $longlist)})->pack;

$mw->Button( -text => "RealLong List", -command => sub{ 
        $dropdown->configure(-choices => $reallonglist)})->pack;

MainLoop;
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