As can be seen in the application log of the KMS server, they can contact each other.
I cannot find KB5003478 in the update log of the KMS server (a dedicated VM), the page you linked links to KB5003217 Preview, which also is not installed.
KB5003478 cannot be found on https://www.catalog.update.microsoft.com/
KB5003217 can be found, but has been replaced by (amongst many others) KB5007266. This KB5007266 has been installed on the system.
The systems says it is fully up to date.
Maybe the system at some point didn't have KB5003217 installed, but installed a more recent version instead. I think this shouldn't matter as the installed KB5007266 replaces this update?
Unless part of the update was lost along the way and is not present in the recent packages.
I've put a new 2022 VM directly on the same LAN for testing, no difference.
DNS resolutions works, powershell Test-NetConnection succeeds:
PS C:\Users\Administrator> powershell Test-NetConnection -ComputerName kms.***.be -Port 1688 ComputerName : kms.kinamo.be
RemoteAddress : 10.x.x.x
RemotePort : 1688
InterfaceAlias : Ethernet0
SourceAddress : 10.x.x.x
TcpTestSucceeded : True
Is there another patch I am missing? If so, where can I download it?