Although my go-to XML module is XML::LibXML, XML::Twig is useful for filtering XML files. The following produces your expected output for the given input:

use warnings;
use strict;
use XML::Twig;
use XML::XPath;  # for findnodes

my $filename = 'foo.xml';
XML::Twig->new(
    twig_print_outside_roots => 1,
    keep_spaces => 1,
    twig_roots => {
        '/TestCode/TestCategory/Test' => sub {
            my ($t, $elt) = @_;
            if ( $elt->{att}{name} =~ /^CheckType_/ ) {
                my @values = $elt->findnodes('./context/value');
                # could theoretically also use XPath for the following
                if ( grep { $_->text =~ /XYZ/ } @values )
                    { $t->flush }
                else { $t->purge }
            }
            else { $t->purge }
        },
    },
)->parsefile($filename);
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