How would a virtual assistant manage an email inbox and filter out important messages?

There are a few ways to go about this. It can be tricky because you need help but you dont want them to have FULL access to your life. Here are a few ideas for you:

Helpdesk Tools (like Zendesk or Freshdesk): If your emails relate to customer inquiries, using helpdesk software lets VAs manage emails through tickets. These tools allow ticket assignment without granting access to your personal email.

or my favorite -

Set up Gmail with Delegation: In Gmail, you can add a delegate, giving them access to manage emails without seeing or accessing sensitive areas (like Chat or Drive). They can read, send, and archive emails but cannot change settings or access confidential labels/folders you don’t share.

We recommend using Ticketing tools to structure your email inbox, so you can easily prioritize, Tag, and Assign to relevant departments/persons.

Ticketing tools help to track the history of emails as well. You can use tools like Freshdesk, Zendesk, etc. 

It helps to make life easier for both client and freelancer / Call centers. 

Thanks