Nikon today seemed to activate Nikon Image Cloud. I can verify that my Z6 III can get to it and access it properly.
That's (most of) the good news.
The bad news is that getting Nikon Image Cloud set up properly is an even bigger warren of thorns and stumbling blocks than SnapBridge. We're talking Access Codes, verifying codes, logging into sites on devices other than your camera, and more. I'm not sure I'm going to be able to document this well in the initial version of my upcoming book, as it appears there are potholes everywhere. For instance, Nikon Imaging Cloud won't allow me to log in with my already registered email address ;~).
But let's get to some specifics. The current Recipes you can download are from Brandon Woelfel, Takahiro Sakai, and Luizclas for portraits; Emilie Hill for travel; Aparupa Day for nature and wildlife; and Danny Gevirtz for video. As an example, Day's only current recipe is Beach Blue, which will put a cyan cast on your photo. Luizclas has four: Red Moose, Purple Mood, Cine Mood, and Blue Mood. My guess is that if you don't like white in your photos, you'll probably love the recipes ;~).
In terms of transfer, what Nikon is offering is a pass through. Your Z6 III can push to Nikon Image Cloud, and Nikon Image Cloud can then further transfer to Dropbox, Creative Cloud, Google (Drive and Photos, both listed as "coming soon"), OneDrive, and Nikon Image Space. This is a 30-day temporary pass through, and requires manual action on your part to complete. Your images are automatically deleted from Nikon Image Cloud after 30 days.
I can't test the firmware download portion, as there isn't an update yet for the Z6 III.
The other good news is that my Z6 III seems to reliably use my home network. Nikon appears to finally have conquered Infrastructure mode (SnapBridge uses Ad Hoc). You have options for connecting only when powered by USB, connecting while the camera is off, and shutting down automatically for inactive connections. In terms of uploading, you can automatically do so, or manually (i-button on playback has a function for sending). You can have the camera upload only raw copies, only JPEG copies, or both when you use RAW+JPEG.
Since the Z6 III supports direct FTP and even through Ethernet (via a USB dongle), if all you're trying to do is get images from your camera to your home computer, there's a better way than using Nikon Image Cloud.