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.