Here is a quick hack that does the job, on a data set that I constructed based on my understanding of your problem statement.

#!/usr/bin/perl
use strict;
use warnings;

my $verbose = 0;

my @lines = <DATA>;

my @items = split /(env\n\s*\{|\{|\})/, join '', @lines;

for (@items) {
    print "###$_###" if $verbose;
}

my $depth = 0;
my $inenv = 0;
my @envblocks;
my @envblock;
for (@items) {
    print ">>>$inenv.$depth---$_\n" if $verbose;
    ++$inenv if ($depth == 0 && /env\n\s*\{/); 
    ++$depth if (/\{/); 

    if ($inenv){
        push @envblock, $_;
        if ($depth == 1 && /\}/) {
            push @envblocks, join '', @envblock;
            @envblock = ();
            --$inenv;
        }
    }
    --$depth if (/\}/); 
    print "<<<$inenv.$depth---$_\n" if $verbose;
}

for (@envblocks) {
    print "===\n$_\n===\n";
}

__DATA__
somestuff
morestuff
env
{
    111
    env
    {
        333
    }
}
and more stuff
and things
zut
{
    222
    env
    {
        444
    }
}
env
{
    777
    env
    {
        555
    }
}
finally a few more things
[download]

and the output - does it look like what you expect?

===
env
{
    111
    env
    {
        333
    }
}
===
===
env
{
    777
    env
    {
        555
    }
}
===
[download]

I won't try to explain it. perlfunc and perlre do a better job of that.
HTH.
Rudif