If a connection is stuck here for more than a couple seconds then that's usually a sign that one of:
- The pop-up window was blocked (although usually you'll get a dialog telling you to enable pop-ups)
- The pop-up window was closed rather than left in the background
- An extension is interfering with the communication between App Inventor and the pop-up window served by the companion app
For the first two, make sure you're allowing pop-ups and that you simply leave the window in the background. If you're doing that, try using an incognito window with extensions turned off to see if you continue to have an issue. If it works in Incognito mode that points to an extension being the problem. If not we can work to try and debug further.