I don't know about GCP logs but you can diagnose where/how DNS requests are handled/directed:
dig -t A a.root-servers.net.
This command asks for an IPv4 address (record -type A) for the host a.root-servers.net (a well known DNS server IIRC - see https://www.iana.org/domains/root/servers)
result:
...
;; ANSWER SECTION:
a.root-servers.net. 421290 IN A 198.41.0.4
...
dig -t AAAA a.root-servers.net.
This requests an IPv6 address (record -type AAAA)
result:
...
;; ANSWER SECTION:
a.root-servers.net. 464385 IN AAAA 2001:503:ba3e::2:30
...
knowing a.root-servers.net. is a DNS server, we can lookup the records stored for another server (starting from one of the root DNS servers)...
dig @198.41.0.4 -t AAAA a.root-servers.net.
Here we are asking DNS host 198.41.0.4 for the address of alias a.root-servers.net. We get an IPv6 response and some additional details
If we have a host name we want to lookup we can check the route to it via DNS servers in the following way:
ping google.com
PING google.com (142.250.178.14): 56 data bytes
64 bytes from 142.250.178.14: icmp_seq=0 ttl=117 time=20.805 ms
lookup DNS server for where the IP address is resolved
host 142.250.178.14
14.178.250.142.in-addr.arpa domain name pointer lhr48s27-in-f14.1e100.net.
We can go to any publicly listed DNS server - e.g. google's 8.8.8.8 (IIRC 8.8.4.4 is also a DNS server run by google) - and we can lookup ANY record to navigate through the DNS servers to find out which DNS server stores our record for the DNS entry we're interested in to see how it gets resolved.
dig @8.8.8.8 -t ANY 14.178.250.142.in-addr.arpa
This returns the list of name servers responsible for domains beginning 14.178.250.*
Result:
...
;; ANSWER SECTION:
14.178.250.142.in-addr.arpa. 21599 IN PTR lhr48s27-in-f14.1e100.net.
...
PTR here just means pointer.
doing the same lookup again: dig @8.8.8.8 -t ANY lhr48s27-in-f14.1e100.net.
We get the result of an A record (IPv4 entry).
...
;; ANSWER SECTION:
lhr48s27-in-f14.1e100.net. 21599 IN A 142.250.178.14
...
This is the IP address for (probably a load balancer for) Google.com.
You can navigate down the initial DNS server, via other DNS servers (there are many) until you get to an A / AAAA Record.