Is it possible to enable breakdown for the duration of updating the project? 

For example, by displaying a message to all users that technical work is in progress, and as a super-admin, you can update and test it until breakdown is disabled.

Or maybe there is a maintenance break plug.
Alternatively, which events should be triggered for Frontend and Backend to display an error page with a given message.

Something like this : gitlab.com/SondagesPro/coreAndTools/maintenanceMode

Thanks, although it's not stable and up to date.

But I will see how to possibly construct my own plug that would work similarly.

unstable ?
It work really good in live project … for big structure.

Except for 5.X