Error install exchange 2016 coexistence with exchange 2010

When installing exchange 2016.

Error: step 7 of 14 mailbox role: Transport service

The following error was generated when "$error.Clear(); 

          if ( ($server -eq $null) -and ($RoleIsDatacenter -ne $true) )
          {
            Update-RmsSharedIdentity -ServerName $RoleNetBIOSName
          }
        ": "Microsoft.Exchange.Data.DataValidationException: Database is mandatory in UserMailbox.
   in Microsoft.Exchange.Data.Directory.ADDataSession.Save(ADObject instanceToSave, IEnumerable`1 properties, Boolean bypassValidation)
   )".

Checking in exchange 2010. I have the following error, in the following Blog FederateMailbox comment on the problem. Also in this other Blog SystemMailbox and Blog DiscoverySearchMailbox

Get-Mailbox -Arbitration | Format-Table Name, ServerName, Database -Auto

Get-Mailbox 

Shows error of objects with server name that does not exist (mail-ex01 server that currently exists)

WARNING: The object contoso.com/Users/SystemMailbox
WARNING: The object contoso.com/Users/FederateMailbox
WARNING: The object contoso.com/Users/DiscoverySearchMailbox

has been corrupted and is in an incoherent state. The following validation errors have occurred:

My query is, delete and recreate does not affect anything. Or fix registry attributes, which would be the most recommended.

Exchange 2010 (Mail-EX01) shows log of an old mail server with the name Mail-EX02.

Exchange 2010 (Mail-EX01 server that currently exists) is running smoothly with 100 users.

I struggled with a similar error when installing Exchange 2019 in an Exchange 2013 environment. It ended up beeing due to RecipientFilterApplied was set to $false.

It was solved by a simple update of the EmailAddressPolicy:

Get-EmailAddressPolicy | Update-EmailAddressPolicy

I noticed that you may have posted the same question in the two communities, it seems that someone has answered it for you in Microsoft Q&A, you could refer to the Microsoft Q&A.

https://learn.microsoft.com/en-us/answers/questions/1337562/error-install-exchange-2016-coexistence-with-excha?comment=question#answers