Have you ever received an email and shortly thereafter, the sender asking you whether you have either read it or even acted upon it? Why should you? It’s just a mail!
Your email client is like your physical mailbox: stuff gets added even without you looking at it. That email that has been waiting in your inbox for three hours or since yesterday evening, is it still urgent? Most likely not.
An email may be important but will never be urgent. Because any form of communication that relies on an asynchronous method of communication e.g. email cannot be urgent. The sender doesn’t even know whether the email was technically delivered correctly.
An IT Manager of mine once said „if it is urgent, then use an instant message, the phone, or your feet and walk over so that you can solve the urgent issue together. But don’t invest time to write an email.“
And he was right.
If your main task is not reacting upon emails, you should switch off any notifications. They distract you from getting your really important stuff done. To be more productive, you should only look at your mailbox a few times. Block some specific time three times a day for triaging your emails using the Eisenhower Method: Since, as I have shown, an email can’t be urgent, is it at least important?
One last thing: The classification whether something is urgent or important to you is your classification and not that of the sender.