Hey everyone,
Just chiming in here since I've been running into the exact same issue! I initially thought it might be a problem with a specific email account or server, but then I realized it's mainly happening with my Microsoft Exchange accounts in Outlook. Interestingly enough, my Gmail account in Outlook is working just fine.
After some digging around, I stumbled upon a solution that seems to work pretty well.
In Outlook, go to Settings > Composing > Wait to send messages for, and increase that interval. I started with 5 seconds, and it definitely helped, but didn't completely eliminate the "Message sending failed" errors. Bumping it up to 10 seconds has almost fixed the issue for me – I still get the error occasionally, but it's super rare now. I'm using Microsoft Outlook 16.87 on macOS Sonoma 14.5, by the way.
Hopefully, this little trick does the trick for you guys too! Let me know if it makes a difference on your end.