If some string like "Now executing cronjob...", "REST call made", "Authorization successful", "Cronjob complete", etc. need to be shown every 1-2 second, what UI elements would you use? I looked at the Material-UI libraries and there's no component for showing transient elements rapidly like that. Most information are shown for 5-6 seconds with the notification UI elements used on most Material-UI components. Also, do you have sources that supports your suggestions?
You can try SnackBar which is a flow-on-top UI indicating some running background tasks and it doesn't block the user's interaction with the rest of the UI.
On desktop, you can position them on the bottom right if it doesn't clash with any existing elements like the Intercom bubble etc, and you might want to color them green for Success/Complete states.