As for the 3rd party menu bar application mentioned by @cho-m:
I developed this in my free time because I wanted an easy way to access passwords, etc. without a browser or the application itself. It is nothing more than the Bitwarden browser extension wrapped in a WKWebView (macOS native WebKit Web View) inside of a NSPopover. As pointed out in this issue, this will not work for the more recent versions of the extensions due to the move from Safari App Extensions to Safari Web Extensions. In short, the communication between JavaScript and the application fails because native messaging is not supported in WebKit (e.g. chrome.runtime.sendMessage does not work).
Thus, I would actually refrain from using this application as it will no longer be updated and is stuck at version v1.48.1. I’m excited of what the Bitwarden team may introduce in the future! 