Preserve search query when using pop out feature

I only use the Bitwarden browser extension because I always have my browser open. So when I need credentials in another app, I use the drag&drop or copy feature to fill in my username/passsword.

I previously used Chromium based browsers where the extension stays open when I focus another window. In Firefox however it closes, so I need to use the pop out feature to avoid searching for the entry over and over again.

Sometimes I type in a search term and then realize that I need it in another window. In this case I have to pop it out and type it in again.

It would be great if the search query (or perhaps also other state) could be preserved for the popped out instance.