Flag or notification when all child tasks are completed for a user story in Azure DevOps

I have what I consider to be a strange setup in Azure DevOps, with many user stories and custom work items that are just sat there. Essentially the Boards aren't being used and as a consequence there's a convoluted customised process that being adopted with little or no movement.

I'm trying to bring order to it and eliminate many of the custom-built stages, and go to a more traditional Kanban board stance. Beginning, middle, end...

One thing I've come across though is that I have two completely separate teams working on the same user stories. How is that updated, and kept relevant? Nobody seems to be able to share that. My thought is that rather than working on the same user story, the teams should instead have a task or several tasks each covering the bit that they're working on - essentially User Story 272 would be a parent of Tasks 21, 39, 40, 4030. That seems to make the most sense to me at least.

What I'd like to do though, is have it so that when the tasks are completed, there's either a notification sent to the person who has the user story assigned to them to tell them this, so that they can move the user story onto the next stage, or the user story moves on itself when the tasks are complete? Is that possible? It goes against the grain a little for me, because I'd want Team A and Team B to talk to one another but that's not possible, so looking for another way to ensure the stories don't get stuck.

is have it so that when the tasks are completed, there's either a notification sent to the person who has the user story assigned to them to tell them this

We could create notification to send email to the personal, for example, send email when the work item Task is completed.

Step:

Open project setting->Notifications->click the button +New subscription->click the tab Work and select the option A work item is changed. Check the pic below. Then the user will receives the email when the work item Task is complete