Are you using Windows 11? If so, that application will no longer be available after you upgrade to 24H2 or later.
Aside from that, there may not be any "normal" methods like keyboard shortcuts available to toggle listening, as given that the WSR application is more aimed towards an assistive context almost everything is intended to be done through voice recognition.
It's also not a normal window, and as such can't really be targeted. Though, as the WSR GUI is normally always drawn over other windows (this would require not having it minimized), you could try using a mouse click on the orb button to toggle the listening state.