I'm having the same problem.
Starting on or before July 17th, when I try to send from any of my aliases using Outlook.com, the Outlook New app, or the Outlook iOS app, the email won't send and gets stuck in the draft folder instead. In addition, when I try to send an email from an alias using the Outlook iOS app, the email shows in the sent folder but doesn't go through. Then, after I check my account using Outlook.com or the Outlook New app, when I go back to my Outlook iOS app, the email in my sent folder has disappeared. This happens across all devices and browsers.
Oddly enough, I'm able to send emails from aliases in the Classic Outlook app with no problem at all.
Update: I've been chatting with Microsoft support for 4+ hours and I've already chatted with 5 tech support reps and am waiting on a 6th. Microsoft doesn't seem to have a clue about this issue.