Know When Something Goes Wrong with Office 365
Office 365 Notification MC196504 tells us that you can configure email notifications for the Office 365 service health dashboard. Email is sent when one of the configured services (like Exchange Online or SharePoint Online) suffer a problem that affect your tenant. This is Office 365 roadmap item 24231.
The feature has been rolled out to tenants with targeted release and should be generally available to all tenants by the end of March 2020 (a curiously extended roll-out period for what seems to be a relatively simple feature).
Email Addresses for Notifications
To set up notifications, go to the service health dashboard (in the modern Office 365 Admin Center) and select Preferences. Then input one or two email addresses of recipients for notifications of service health updates (Figure 1) along with the set of services for which you want to receive updates.

The SMTP email addresses don’t have to be part of Office 365 and don’t have to be for personal recipients. You could set up one address that is outside Office 365 and another address for a distribution group or Office 365 group. Of course, the hope is that the email services you choose to receive notifications remain unaffected by an outage!
There’s no way to configure these settings except through the Office 365 Admin Center.
When Notifications Arrive
Notifications arrive soon after Microsoft declares that an incident exists. This could be some time after people start being aware of a problem as Microsoft needs to investigate problem reports and gather some data before they are sure that an incident really exists. And as you can see from Figure 2, some emailed notifications arrive after the incident has been resolved and service is restored.

From a phishing perspective, service alerts come from O365mc@microsoft.com and never ask an administrator to do anything like input their credentials. These notifications are simply informative. After all, if something breaks inside Office 365, all you can do is sit back and wait for Microsoft to fix the problem.
Even the most experienced Office 365 administrators sometimes need a helping hand to master the intricacies of the service. Or just small and simple changes like this that add a lot of value. Subscribe to the Office 365 for IT Pros eBook to make sure that you stay informed.
It would be nice if you could get more granular with the alerts, such as getting notified for Incidents vs Advisories. Then also filter by status. From my testing on a targeted release tenant, I’m not getting an email notification for advisories.
Would be great if you can get a RSS feed, then setup a page on your Sharepoint somewhere to keep track of it all (obviously in outlook as well for when Sharepoint is offline)
You could use the code explained in https://thingsinthe.cloud/Teams-message-cards-Office-365-Health-status/ to grab health information from Office 365 and instead of sending it to Teams, post the items to SharePoint.