Substitute variable names with previously read values. This requires V1 to have been defined before V2, etc.:

use warnings;
use strict;

my %vars;
while (<DATA>) {
    chomp;
    s/\$(\w+)/exists $vars{$1} ? $vars{$1} : die "Error: no env var $1
+\n"/ge;
    my ($key, $value) = split(/=/, $_);
    $vars{$key} = $value;
}

use Data::Dumper;
$Data::Dumper::Sortkeys=1;
print Dumper(\%vars);

__DATA__
V1=/home/user
V2=$V1/test
V3=$V2/file.txt
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Outputs:

$VAR1 = {
          'V1' => '/home/user',
          'V2' => '/home/user/test',
          'V3' => '/home/user/test/file.txt'
        };
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