I use the pop-out button as suggested by @dunxd (and a second monitor). Speaking to the feature request though, I’m not sure the browser extensions can be made to stay open (‘stay on top’) after you click on the web page. 
Edit: I wanted to clarify what do you meant by ‘same folder’? If you mean you’d like to have the same view and quickly use the same login/pass, and the act of searching for it is the step you’d like to cut out, then I would ask if your logins have a URI set, and if it’s scoped to ‘base domain’ or ‘host’? For me, on this site for example, I have only my login for ‘community.bitwarden.com’ being suggested when the extension is first opened, and my ‘bitwarden.com’ is not listed there. Does that make sense?