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 admin menu bar entry labeled "My Website" and inspect how that link is rendered. Done means selecting it opens the site in a separate browser tab while preserving the current admin panel view; no specific file or test is identified in the issue.

Written by the indexing model from the issue text.