Currently, there's no way to disable scenario notifications for your own scenarios. These notifications can stack up quickly and cover up large parts of the UI. In some cases, their links are also dangerous, since users can easily lose unsaved work by accidentally clicking them when they pop up. This happened to me recently, after spending about 30 minutes renaming imported datasets on the dataset import screen, a burst of notifications covered up the next text box just as I was clicking it and I was instantly navigated to the log for my scenario, resulting in a lot of lost work naming the datasets (about 200 datasets being converted to semantic names). In general, these notifications constantly cover up the UI, since my scenarios run frequently.
It would be great to have an option to suppress these notifications in profile settings.
Alternatively, if there were a way to disable the toast popups but keep them in the notifications tab (and just increment a badge number on that tab instead), that would also be great.