The Z 6 III was added to Nikon's resource download site:
https://downloadcenter.nikonimglib.com/en/products/629/Z6III.html
Currently, one can only download the N-Log Video Technical Guide (in the 'Manuals' tab), NX Studio and the N-Log 3D LUT (in the 'Software' tab), but this is where the user manuals and firmware updates will be posted for the camera in the future.
The Z 6 III is now available in the Nikon Digitutor:
https://imaging.nikon.com/imaging/support/digitutor/z6iii.html
The User's Manual and the Reference Guide are now available in the 'Manuals' tab.
Self service repair for the Z 6 III: https://ssr.downloadcenter.nikonimglib.com/en_US/products/34/Z6III.html