The following code creates a clean merger of the two hashes as a tree ( or rather directed graph) structure, i.e. it's not assuming that the input is not buggy.

The resulting merger can easily be post processed to create the desired output.

FWIW:

Instead of an recursive algorithm, I used the power of cross-references and auto-vivification.

This allows to handle possible loops in the input, without risking a non-halting recursive call.

use strict;
use warnings;
use Data::Dump qw/pp dd/;

my %pid_tree;

my %process_data = (

              '56061' => {
                           'parent' => 'NA',
                           'name' => 'file1'
                         },
              '56069' => {
                           'parent' => '56065',
                           'name' => 'echo Hello_file1'
                         },
              '56062' => {
                           'parent' => '56061',
                           'name' => 'echo Hello_file2'
                         },
              '56065' => {
                           'parent' => '56061',
                           'name' => 'file2'
                         }
                   );

while ( my ($pid,$h_pid) = each %process_data ) {
    my ($parent,$name) = @{$h_pid}{qw/parent name/};

    $pid_tree{$pid}{name} = $name;
    $pid_tree{$pid}{pid}  = $pid;
    push @{ $pid_tree{$parent}{children} } ,$pid_tree{$pid};
    
}
$pid_tree{NA}{name}= undef;
$pid_tree{NA}{pid}= "NA";





my %files_data =
  (
   './GetOpt.pm' => {
                     'pid' => {
                               '56061' => 1,
                               '56065' => 1
                              }
                    },
   'file1' => {
               'pid' => {
                         '56061' => 2
                        }
              },
   'file2' => {
               'pid' => {
                         '56065' => 2
                        }
              },
   './src/bin/perl' => {
                        'pid' => {
                                  '56061' => 1,
                                  '56065' => 1
                                 }
                       }
  );

while ( my ($file,$h_file) = each %files_data ){
    while ( my ($attr, $h_attr) = each %$h_file ){
         while ( my ($pid, $pid_count) = each %$h_attr ) {
             #print "$file $attr $pid $pid_count\n";
             next if $file eq $pid_tree{$pid}{name};
             push @{$pid_tree{$pid}{files}},$file
         }
    }
}

pp $pid_tree{NA};
[download]

OUTPUT

{
  children => [
    {
      children => [
        { name => "echo Hello_file2", pid => 56062 },
        {
          children => [{ name => "echo Hello_file1", pid => 56069 }],
          files => ["./src/bin/perl", "./GetOpt.pm"],
          name => "file2",
          pid => 56065,
        },
      ],
      files => ["./src/bin/perl", "./GetOpt.pm"],
      name => "file1",
      pid => 56061,
    },
  ],
  name => undef,
  pid => "NA",
}
[download]

NB: I had to repair corrupted input from the OP. Again.