Not sure if you'd consider this an app or an extension issue...
I'm using app version 5.2.6 and extension version 1.6.2 (running in Chrome Version 121.0.6167.184).
When I launch the (paired) extension to contact my phone for a code, the notification is nearly always received and displayed if the app isn't running or in the foreground. However, if the app is already "up" on my phone and displayed, I seldom get a notification from the extension - the "Notification" section in the app is also empty when this happens. If I close the app and re-click from the extension. then I get the notification and everything works as it should...