Note: Might be easier to install the admx admin templates to Group Policy Editor. See this post for more info

Office 2019 annoyingly wants you to sign in to either a domain or the cloud. It shares the same registry space as Office 2016, so the procedure is:

Preparation:

1. Note that this must be done on a per-user basis, for anyone who logins into the machine. So 2 users on the same machine = do it twice. Or if that user signs into another machine, do it again.
2. Go into one of the Office apps, go to Account, and select “Sign out” & then click Yes when prompted.

First, close all Office applications:

Word
Excel
PowerPoint
Outlook
etc.

Second, open the Registry Editor: (may need to Run As Admin)

Start > Run > regedit

Third, navigate down the tree:

HKEY_CURRENT_USER
SOFTWARE
Microsoft
Office
16.0
Common

Third, add the SignIn folder:

Right-click on the Common folder
Go to New > Key
Name it “SignIn” (without the quotes)

Fourth, add the registry key to disable the sign-in option:

Right-click on the SignIn folder
Go to New > DWORD (32-bit) VALUE
Name it “SignInOptions” (without the quotes)
Set the value to 3

Fifth, verify that it worked:

Open up Word
It should no longer have the “Sign in” button in the top bar
Under File > Account, all of the sign-in verbage should be gone

If you ever need to add it back in, just delete the SignInOptions reg key!

Source: Question – Tutorial: Disable the Cloud sign-in option on Office 2019 | AnandTech Forums: Technology, Hardware, Software, and Deals