Update For best solution, see Answer by Burmistrov.
As for launching the app causing a page to open in your default web browser, Yes, that is the new normal.
Per an email on the psgsql-announce email sent by Dave Page on 2018-04-13:
The desktop runtime now runs as a system tray application and utilises the browser on the system to display pgAdmin. This resolves numerous bugs and issues caused by QtWebKit/QtWebEngine.
As for the app doing nothing when launching after closing the first web browser window, one workaround: Bookmark the URL.
Here is an example of such a URL:
The port number, 58353 in the example above, varies arbitrarily. To discover the port in use currently, do a port-scan.
Kill the pgAdmin server process
The pgAdmin 4 app is actually architected as a web app running inside a bundled web server. So the port number listed above is the port on which that bundled web server is listening.
So one workaround to our re-open-app problem is to kill the process of the web server of pgAdmin. Then run the pgAdmin 4 app again to re-launch the bundled web server, re-create the
pgAdmin 4 process, and have your default web browser open a fresh window.
Yes, pgAdmin 4 is annoying in this regard and in other regards as well. You may want to pursue using alternate admin tools. There are many to choose.