In addition to having a modern design, the Outlook icon is yellow. That would be a return to form since the Outlook icon was changed from yellow to blue over a decade ago. As far as I can tell ...

Google is now updating the icon so that there are no longer four solid color sections. Instead, red bleeds into yellow, yellow into green, and green into blue. It looks more vibrant and colorful.

As for actually using the yellow Outlook icon, you may have more luck switching to it for Outlook (classic). The new Outlook is a store app, so customizing its icon is tricky.