Since the browser add-ons got an overhaul, when looking up an entry, the last entry will stay open if I open the add-on again. Is there a way to prevent this?
99% of the time when I look up and entry or edit one and close it, I don’t need it anymore. It’s kind of annoying always switching back to the main overview to select a different one…
Returning to where you left off is the first step to address a concern where data is getting lost because people need to reference the underlying window. Here is the feature request for that. There is a timer which attempts to balance between this and your goal by returning to the “home” page if it has been a while since the extension was opened.
There is not currently a way to adjust this timer. Perhaps you could submit a feature request here on the community to either zero the timer (as you suggest, above), allow one to configure the timer, or to add a home button (as someone else suggested, but not as a feature request).
Do you have direct evidence for this (source code, release notes, official statements)?
In my experience, the main thing that returns the extension state back to the default Vault view is if you switch to a different browser tab (even if you switch back to the previous tab afterwards).
Just personal observation.
I opened my browser extension, nagivated to settings >> notifications. Then, momentarily closed (by clicking elsewhere on the web page) and then reopened the vault. It remained on notifications.
I then closed it again, but waited a few a few minutes and instead of opening to notifications, it opened to vault.
Thank you . I guess I was not sufficiently patient to wait for the timeout previously. 
This time, I refrained from switching browser tabs (or opening the extension) for 2 min, and I can confirm that at some point during that interval, the browser extension does reset itself to the default Vault view.