There used to be several (not necessarily all at the same time, this is from git log -p):
ext.echo.overlay.beforeShowingOverlay
ext.echo.special.onInitialize
ext.echo.special.onLoadMore
ext.echo.updateNotificationCount
Now, there are none (we should take into account this is part of our public API, when designing them, and making changes).
We should consider which to add (not necessarily the same as before).
@Quiddity raised a use case for this, marking as read when you open the flyout, as a user script. T146294: Make a way for editors to have notifications automatically marked as read, when a flyout is opened