Hello steeledavis,
Thank you for posting in the Apple Support Communities. We know how important notifications are, and we'd like to help.
First, Microsoft Teams is only compatible with iPhone, iPad, and iPod Touch running iOS or iPadOS 12.2 or later. This may be why you're not seeing the app installed on the Apple Watch.
App Store Preview: Microsoft Teams
As for notifications, we recommend reviewing the notification settings for that specific app on your iPhone, and checking to see if Do Not Disturb is enabled for the Apple Watch. The Apple Support articles below explains these steps in more detail.
Change the audio and notification settings on your Apple Watch
Change notification settings on iPhone
Also, notifications will go to your Apple Watch if your iPhone is locked or asleep. Learn more here:
Notifications on your Apple Watch
Lastly, iOS 15 introduces Focus, which temporarily silences notifications for certain apps that aren't allowed during an active Focus schedule. You can check to see if you have Focus enabled in Settings > Focus. Check this out to learn more:
Use Focus on your iPhone, iPad, or iPod touch
Let us know what you find out. Kind regards.