Essentials is dead. Long live WHS 2011! ha ha
I'm sorry to say that I can confirm the issue. I forced an Essentials 2016 install onto a different public IP (cell phone hotspot) and sure enough, dynamic DNS broke. Note that External IP is blank, which would seem to indicate failure retrieving the public IP address:
[61048] 220507.135925.7819: ConnectivityCenter: DomainNameResolveableInfo.ExternalIP:
[61500] 220507.135925.7919: ConnectivityCenter: Job finish. Result: Success
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[62104] 220507.135925.9009: ConnectivityCenter: Suggestion: An error occurred while updating the dynamic DNS information for your server with the information that you gave your domain name service provider. Please try again later. If this problem continues, contact your domain name service provider for support.
[62104] 220507.135925.9009: ConnectivityCenter: Overall status: Error
[62104] 220507.135925.9009: ConnectivityCenter: Properties updated.
[62264] 220507.135925.9099: ConnectivityCenter: DomainNameResolveableAnalyzer: Domain name could not be resolved to router's external IP address, should be manual fixed
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[62264] 220507.135925.9099: ConnectivityCenter: Overall status: Error
[62264] 220507.135925.9099: ConnectivityCenter: Properties updated.
I'm going to try a Wireshark trace to see if I can figure out what the problem is, but at some point, the cost of compensating for Microsoft's lack of support outweighs the benefits.