Hi @Schindler Christian ,
If after the migration is complete, you do not uninstall Exchange 2013 and maintain the coexistence state, then you need to enable ADFS for all Exchange organizations, not only for Exchange 2019 .
If you uninstall Exchange 2013 after migration, only Exchange 2019 will exist. It is achievable, you can follow the steps in the link you provided. If you want to set up a specified server, please enter the url entered during the setting process as the address of a special server, and when configuring Exchange for ADFS, please configure it on the specific server.
It should be noted that the "steps 4a: Create relying party trusts in AD FS for Outlook on the web and the EAC" and "4b: Create custom claim rules in AD FS for Outlook on the web and the EAC" need to be executed twice. Respectively for OWA and ECP. Then configure the Exchange organization to use AD FS authentication.
Then run the following command lines to configure the authentication method of ECP and OWA's virtual directory. It should be noted that, please configure ECP first, and then configure OWA.
Finally, please run the IISRESET in CMD start as administrator to restart the IIS.
Get-EcpVirtualDirectory | Set-EcpVirtualDirectory -AdfsAuthentication $true -BasicAuthentication $false -DigestAuthentication $false -FormsAuthentication $false -OAuthAuthentication $false -WindowsAuthentication $false
Get-OwaVirtualDirectory | Set-OwaVirtualDirectory -AdfsAuthentication $true -BasicAuthentication $false -DigestAuthentication $false -FormsAuthentication $false -OAuthAuthentication $false -WindowsAuthentication $false
----------
If the response is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.