The way Perl treats hashes and hash references can be confusing at first - what you are dealing with in this structure is an array reference which contains a list of hash references, and you need to know how to de-reference the structure. These changes to your code should help:

for my $input ($form->inputs) {
    if (q{FileName} eq $input->{name}){
        print Dumper($input); # Show First output block
        
        my $hash = $input->{menu}[0]; # '$hash' not '%hash'
        # $hash is the first button
        print Dumper($hash);
        
        # to iterate the radio button values
        my $menu = $input->{menu};
        for my $button ( @$menu ) {
            my $file = $button->{value};
            print "$file\n";
        }
    }      
}
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