@dln949 As far as I know, Anbox for the time being only gets network connectivity interaction with the Linux system, no notifications, GPS, audio, or any other interaction with the phone components.
Native applications do get notifications, and webapps should get them if they get notifications in the desktop, but for that you should use UT Tweak Tool to get the webapp to run in the background and you should not close it. In any case I don't think one can rely on those notifications from webapps, if they work at all.