What version of the browser extension are you using, and how are you opening the extension in a browser tab? Normally, the browser opens in a pop-up viewport that is not a browser tab. If you use the pop-out function, you can open the extension in a new browser window, but not in a separate tab within your current browser window.
Older versions of Bitwarden did use to open a new browser tab under certain circumstances (e.g., when attempting to autofill while the vault was locked), and at the time, I posted a feature request similar to yours:
(the above feature request was closed when Bitwarden changed its method for handling such unlock scenarios).
Please explain in a little more detail how you are using the browser extension.