How can I copy the email address of the recipient when I compose a new email in Microsoft Outlook for Android?

You can't copy email addresses that are already "formatted" as in your image when using Outlook for Android. While other email apps offer this basic feature, Microsoft simply does not implement it.

You must either enter the full email manually then copy it. Or search for the email (using the search tool), when found, click on the email address next to the envelope. A window will appear with "Copy" as an option.