Failed Activity Doesn't Trigger Teams Alert

Can you share the overall Pic of the pipeline?

When you have multiple dependencies set across for diff activities to an activity,it functions as an AND.
Meaning team activity would be executed only if Set variable activity fails AND whatever conditions you have added for other activities 

Hello 4iurchenko! 

As it shown on your screen, you have lots of other activities befor the messaging, so they are all to be completed (or failed) to fire the message.

To solve it properly you have multiple options:

1. Set Teams message after each action, so then you will capture and deliver error message for all of them.

2. Have some variable to aggregate error messages into one body and then at the end of your pipiline (On completion) you can evaluate if it's not empty and post message.

Could you please check and reply if that what you are looking for?

BR, Taras