Open "My Website" from Admin Menu Bar in a New Tab

Is your feature request related to a problem? Please describe.
Yes. It's a bit inconvenient when I click on "My Website" from the admin menu bar and it opens in the same tab, disrupting my workflow in the admin panel.

Describe the solution you'd like
I would like the "My Website" link on the admin menu bar to open the site in a new browser tab instead of the same tab.

Describe alternatives you've considered
As a workaround, I currently right-click the link and select "Open in new tab," but this slows down the process and isn't very intuitive for all users.

Additional context
This small change can improve usability for admins who need to toggle between the backend and frontend frequently without losing their current admin panel view.

Start at the React frontend entry point for the admin menu bar and locate the "My Website" link. Verify its current navigation behavior in a browser; done means selecting the link opens the site in a new tab while leaving the admin panel open.

Written by the indexing model from the issue text.