Greetings from Dublin 
@Erwin_van_Dijk and welcome to our Community!
We recently launched a new Do not Disturb feature in Asana, and for technical reasons we had to remove the “Snooze Inbox” feature. We’ve received similar feedback in the announcement post linked above, so thank you so much for creating this #productfeedback thread. This will help us collect feedback and report to our Product Team to take on board for future iterations.
We will update this thread as soon as we have some updates on our end, but in the meantime, I would recommend keeping your sidebar closed when you don’t need it, it won’t totally solve your issue since the dot will still appear in your browser’s tab, but it will help reduce visual noise. Remember you can easily open/close your sidebar using the “TAB+O” shortcut.
Hope this helps!