Thanks @nem5ac3 for the report,
Can you help check the following:
1) Do notifications and new messages work properly on Chrome?
2) If another user is away for more than 5 minutes, do their status properly change on the desktop app to 'away'?
3) What is your Mattermost server version in Main Menu > About Mattermost?
4) What is your desktop app version from Menu Bar > Help > Version?