@jdaviescoates got it! It was the IP allowlist.
Last week I noticed a cloudron error that said:
Server is running out of disk space 2:30 PM
One or more file systems are running out of space. Please increase the disk size at the earliest.
/dev/root is at 97% capacity.
So I attempted to make my EC2 instance bigger (didn't solve the space problem, but that's for another thread). It did however change my IP address. I added the new IP to Mailgun and swaks started working properly in a few minutes.
Side note: @crazybrad I think we're mixing up marketing/bulk and transactional. I use transactional for my ghostcms so I can keep things behind an auth wall, trying to keep kids safe. My parents/members use it rarely, it's not even worth $12/mo compared to mailgun's transactional email cost which is cents/mo.
Thanks to all for the help.