Shimano Nexus 8 internal hub skip/clacking noise when under torque
There are some Nexus and Alfine bikes that have made it out into the world with a spec mismatch between the over and under style cassette joints and the shifter.
The cable pull sequence works in reverse order between the two shifter types. Because the cable pull for this system varies with each click, everything gets screwed up if you then use the setup marks. Something like what you're experiencing can result.
To check this, get your exact cassette joint and shifter models and make sure they're listed as compatible on si.shimano.com.
If that checks out, test it with less belt tension.
If that's not it, get oil dunk gear and the Nexus/Alfine notchy tool, pull the core, wipe, inspect for anything out of place or prematurely damaged or worn, dunk, grease, reassemble, and see if that fixes it.
One perfectly likely explanation is that the pawls that drive the shell are having engagement problems. If one or more is under-lubricated, deformed, or out of place, it could cause a partial engagement problem, which also fits the symptoms. This can lead to a situation where the tips of the pawl(s) get damaged and the problem gets worse. This is easy to inspect for once the core is removed. Note that despite the ostensible complexity of the hub, the pawl system in question is the most exposed part of the whole deal, being the interface between the drive ring inside the hub shell and everything else. If it does the same behavior with the cable disconnected completely, I think this pretty likely is what's happening.
It is true that everything about this should be covered under warranty. Between parts shortages and the usual awkwardness of getting warrant support to happen for mail order bikes, it may get hairy at the moment.
Also check dropout alignment slash sync up slider fore/aft if applicable, all of which can in theory cause hub badness.