Project can customized, via an accepted process, see here. This is so for all MS office applications, i.e., Outlook.

Sharepoint may be part of the solution, but there are also other ways. A lesser intusive way (than custom coding) that comes to mind is using Outlook forms. Such that a change by an approved user in a Project plan automatically generates and populates an Outlook Form, which is then emailed to whoever. The emails could be made to be partially invisible to users (in the same way Outlook meeting requests are email, but then you don't have to deal with them after you accept the request), i.e., you'd click on a button labeled Process Project X updates.

Creating a chronological history of changes is doable with a little more work.