does not access the domain with the proxy enabled

[Vysokostnyi]

the domain does not work if the proxy is on, and if I turn it off, everything works

[mrikirill]

It wouldn't work, because with proxy the script sets your proxy server ip address as A record which is non of your NAS ip address. None of DDNS services would work with proxy in this case. You can make a modification that the script can bypass proxy while ip adress detection to get your NAS ip address and set it to CF