Kyle,
There is no current setting to make Attach as Copy the default in either OWA or New Outlook. If you want the team to add this, please submit feedback via Help, Feedback in New Outlook.
In the meantime, you can choose to attach a copy each time you attach a file. It's not super obvious, but in my example below I am attaching a file to an email in New Outlook and after I select the file, I click the dropdown for Share Link and click Attach to attach a copy.