You are missing a dollar sign before the variable name.

You cannot use if in an expression, but you can use the Conditional Operator (aka the Ternary operator):

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

use Data::Dumper;

my $group = 'g';
my $exe   = 'e';

for my $s_version (qw(s8 s9)) {
    my $template
      = { global => {
                     variables => {
                                   version => "${s_version}",

                                   ($s_version eq "s8")
                                       ? (base => "\${version}/$group"
+)
                                       : (
                                          exe  => "\${exe_state}",
                                          base => "\${s_version/${exe}
+/$group"
                                         ),

                                   variant =>  "10",
                                   dir => "\${root}",
                                  },
                    },
        };

    print Dumper $template;
}
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Update: code formatting.