I have come to discover that the "when a new email arrives" trigger is bugged when the email that arrives in your inbox has been sent to a distribution list that you are a member of rather than directly to you. It is critical that this function be implemented, for a variety of uses:
In my use case, we have a helpdesk distribution list, where a service account is a member. We are configuring an automatic reply system to respond back to the sender from the service account with frequently asked questions and self-service answers when a new email is sent to the helpdesk distribution list. Power Automate is necessary for generating different messages based on whether the user is internal or external to the organization, what their job title is, and what time of day it is. We plan on developing this for more automation, sentiment analysis, and the development of a full helpdesk ticketing environment.
Other use cases can be to create SharePoint list items or tasks based on emails sent to distribution lists. Currently, this is all unobtainable, as the application is limited in this regard.