Can confirm, this is quite easy to reproduce. Additionally, it seems that Steam has issues of detecting which application is in foreground if you open more non Steam applications, and if you are using different perfomance profiles per application you can find yourself the Deck playing games with a 4 W profile dedicated to the browser and force you to reselect the launched application in the SteamUI. Quite annoying.
Can confirm this behaviour has been fixed on latest steam deck client stable channel.
Fixed on my side
Nothing extracted yet.
To reproduce:
This is incorrect behavior, we are supposed to enter Firefox once it's launched.
The environment I tested on was Steam Deck OLED 512 GB, running SteamOS 3.6.8 in Game Mode.