I've been having this issue for the past few months (had been using Outlook in browser in the interim) and have only gotten around to addressing it now.
I went to Options > Message Arrival tab and it's set up as follows,
None of the selected features occur when I receive an email and I've taken to wearing a headset at all times in order to hear the notification when I receive an email in my web version of Outlook.
In addition to the notifications issue, Outlook is extremely slow on opening (and has been for 12 months plus), and regulalry freezes when navigating between emails.
I have a E3 M365 license and am on the Enterprise Monthly channel, however, the current version is 2311, and we are unable to update (despite more recent versions being released).
Some of these issues existed prior to this update though so don't think I can blame it solely on lack of update, and it's only 5 months out of date.
I uninstalled O365 suite using scrubbing tool today and reinstalled and this hasn't solved any of the issues.
We do have add-ons which slow Outlook down a bit (1 mandatory slows it 2/3 secs on opening) but sometimes I'm waiting a minute before being able to switch between emails, and even then, I have to leave deliberate pauses between each email otherwise it'll freeze.
If anyone has experienced this or has any advice I'm all ears.
Thanks in advance,
Chris