There are many ways in PowerShell to check the mailbox database copy status in Exchange, here are some examples from the Exchange Management Shell (EMS):

Blanket check.
Per DAG check.
Per Server check.

  • Get-MailboxDatabaseCopyStatus *

The above command runs across all servers and databases in the environment. Below is the next example.

  • Get-MailboxDatabaseCopyStatus -Identity dag1*

The above command only runs against a specific DAG name, in this example DAG1. Below is the next example:

  • Get-MailboxDatabaseCopyStatus -Server Mailbox1

The above command runs against a specific server to see its mailbox database copy status.

Hope it helps.