I believe what you're seeing is normal behavior. If you ran that query
against a TLD you'd get the NS servers of the TLD in the answer
section but I don't believe it works that way when delegating
subdomains.
I just tested in my environment and when I query an a-record in the
delegated subdomain the proper NS records appear in the authority
section but I do not get a response querying for NS records directly
against a delegated subdomain.
[root@ns1 ~]# dig test.ad.example.com; <<>> DiG 9.11.21-RedHat-9.11.21-1.fc32 <<>> test.ad.example.com;; global options: +cmd;; Got answer:;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 56885;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 1, ADDITIONAL: 2;; OPT PSEUDOSECTION:; EDNS: version: 0, flags:; udp: 4096; COOKIE: bcf0f0a951a4c7fc9bac74fd5f29c35a5305f69d279f3827 (good);; QUESTION SECTION:;; ANSWER SECTION:;; AUTHORITY SECTION:;; ADDITIONAL SECTION:;; Query time: 0 msec;; SERVER: 127.0.0.1#53(127.0.0.1);; WHEN: Tue Aug 04 13:21:46 PDT 2020;; MSG SIZE rcvd: 126
[root@ipa1 ~]# dig dc1.ad.cloud.chx; <<>> DiG 9.11.4-P2-RedHat-9.11.4-16.P2.el7_8.6 <<>> dc1.ad.cloud.chx;; global options: +cmd;; Got answer:;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 64904;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 0, ADDITIONAL: 1;; OPT PSEUDOSECTION:; EDNS: version: 0, flags:; udp: 4096;; QUESTION SECTION:;dc1.ad.cloud.chx. IN A;; Query time: 13 msec;; SERVER: 127.0.0.1#53(127.0.0.1);; WHEN: Tue Aug 04 13:24:16 PDT 2020;; MSG SIZE rcvd: 45[root@ipa1 ~]# dig cloud.chx AXFR | grep dc1ad.cloud.chx. 86400 IN NS dc1.ad.cloud.chx.dc1.ad.cloud.chx. 86400 IN A 192.168.1.253