As relevant to “Group tasks into themed days for batch processing” point (1st point)
Formal is a messaging app delivers messages only three times a day in batches.
Learn more about how it works at https://www.formalapp.com
Unlike Email, Formal holds the messages on the Sender’s queue until Receiver’s receive time reaches.
It not only free the Receiver from interruption it also clarifies the reply expectation time of the Sender.
“Text messages and emails might seem harmless, but they can drag your attention away from the task at hand. Set your devices on airplane mode”
In Formal, There is no need to turn off notification or closing the app is needed. (For example, you can keep open the app to search some early messages)
Disclosure: I am a developer at Formal. Sorry to post a promotional comment.