Here's my guess as to what you want, at least it gets the directories you showed.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11130470
use warnings;
use JSON::PP;

my $j = '{ "/": { "type": "dir", "files": [ { "p": { "type": "dir-link
+",
"source": "/nfs/data/project", "files": [ { "xa": { "type": "dir", "fi
+les":
[ { "tools": { "type": "dir", "files": [ { "sd": { "type": "dir", "fil
+es": [ {
"su2av": { "type": "dir", "files": [ { "duf": { "type": "dir", "files"
+: [ {
"0.4.0": { "type": "dir-link", "source": "/nfs/vsa/project/xa/vuvua/su
+2av",
"files": [ { "bin": { "type": "dir", "files": [ { "duf": { "type": "li
+nk-file",
"source": ".run" } }, { ".run": { "type": "file" } } ] } } ] } } ] } }
+ ] }
} ] } } ] } } ] } } ] } }, { "nfs": { "type": "dir", "files": [ { "dat
+a": {
"type": "dir", "files": [ { "project": { "type": "dir", "files": [] } 
+} ] }
}, { "vsa": { "type": "dir", "files": [ { "project": { "type": "dir", 
+"files":
[ { "xa": { "type": "dir", "files": [ { "vuvua": { "type": "dir", "fil
+es": [ {
"su2av": { "type": "dir", "files": [] } } ] } } ] } } ] } } ] } } ] } 
+} ] } }';
my $obj = decode_json($j);

my $alltypesref = findtypes( $obj );
use Data::Dump 'dd'; dd $alltypesref;

sub removeprefixes
  {
  local $_ = join "\n", grep $_ ne '/', (sort @_), '';
  s/^(\N*)\n(?=.*^\1\/)//gm;
  split /\n/;
  }

sub findtypes
  {
  my ($obj) = @_;
  my $types = {};
  findpath($obj, '', $types);
  $types->{dir} = [ removeprefixes @{ $types->{dir} } ];
  return $types;
  }

sub findpath
  {
  my ($obj, $path, $types) = @_;
  for my $name ( keys %$obj )
    {
    my $info = $obj->{$name};
    push @{ $types->{$info->{type}} }, my $new = "$path/$name" =~ tr[/
+][]sr;
    findpath( $_, $new, $types ) for @{ $info->{files} };
    }
  }
[download]

Outputs:

{
  "dir" => [
    "/nfs/data/project",
    "/nfs/vsa/project/xa/vuvua/su2av",
    "/p/xa/tools/sd/su2av/duf/0.4.0/bin",
  ],
  "dir-link" => ["/p", "/p/xa/tools/sd/su2av/duf/0.4.0"],
  "file" => ["/p/xa/tools/sd/su2av/duf/0.4.0/bin/.run"],
  "link-file" => ["/p/xa/tools/sd/su2av/duf/0.4.0/bin/duf"],
}
[download]