I prefer parsing the whole file into a Perl structure and then read the information from there. By modifying the second regex you could also only read the ip addresses: /^\s*set\s*(ip)\s*([.0-9]*)/.

use strict;
use warnings;
my @data;
while(<DATA>){
  push @data, { 'edit' => $1 } if /^\s*edit\s*"(.*)"/;
  $data[-1]{'set'}{$1} = $2 if /^\s*set\s*(\w+)\s*(.*)/;
}
defined $_->{'set'}{'ip'} and print "$_->{'edit'}: $_->{'set'}{'ip'}\n
+" for @data;
__DATA__
config system interface
    edit "dmz"
        set vdom "root"
        set ip 192.18.254.1 255.255.254.0
        set allowaccess ping fgfm
        set type physical
        set alias "Guest-Wlan"
    next
    edit "wan2"
        set vdom "test"
        set ip 10.4.254.198 255.255.255.252
        set allowaccess ping https ssh snmp
        set type physical
        set alias "To MON ospf int"
    next
    edit "wan1"
        set vdom "root"
        set ip 1.1.1.1 255.255.255.252
        set allowaccess ping https
        set type physical
        set alias "To Internet"
    next
    edit "modem"
        set vdom "root"
        set mode pppoe
        set allowaccess fgfm
        set type physical
    next
    edit "ssl.root"
        set vdom "root"
        set type tunnel
    next
    edit "ssl.MyRealm"
        set vdom "MyRealm"
        set type tunnel
    next
    edit "internal1"
        set vdom "root"
        set ip 10.1.16.3 255.255.255.0
        set allowaccess ping https ssh snmp fgfm
        set type physical
        set alias "To MON Internal "
    next
  edit "internal2"
        set vdom "MyRealm"
        set dhcp-relay-service enable
        set dhcp-relay-ip "192.168.1.1"
        set ip 192.168.2.1 255.255.254.0
        set allowaccess ping https ssh snmp fgfm
        set type physical
        set alias "To MINE"
    next
    edit "VPN-Dial"
        set vdom "root"
        set type tunnel
        set interface "wan1"
    next
end
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