Active Directory migration from Windows 2003 to Windows 2016

while single-label domain are deprecated, I really need to keep it running as-is. I evaluated both a domain rename and/or a domain migration to a new name, but they simply seem too much to ask for my customer.

The right thing is sometimes the hardest. IMO, you're doing your customer a disservice by continuing to use and support the SLD. Do the "right" thing and perform a domain rename or migrate to a new domain.

on the new Windows 2016 server, use "Active Directory Sites and Services" to remove any eventual leftover from the demote operation

A side note, a left over I always have to clean when I migrate a 2003/2008 is within the DNS's console, the old DC is always still listed in the NS's field.

As there to be exact;

A second note I would make sure they don't use WINS too. Please double check there to be sure if you need to activate that or not, it was popular in those years.

For the domain rename I dont recommand it, it's a big task to do that can leave many error behind if a bad step is done.