Running an email service is not, by any means, a 'tiny project'. I would never pay, nor rely on an e-mail service that is effectively a one-men side project.
I just took a quick check on the 'mailbox' domain (I can't paste emoji here on HN). There seems to be no DMARC, no MTA-STS and no TLS-reporting set up for these domains. The SPF record allows a single /48 (65k) IPv6 block of addresses to send email on behalf of the domain. The MX does not seem to support TLS. The SPF record seems to be added at the '@' domain, so it is returned on every query, even where it is not supposed to be returned, so you can be sure DKIM will fail (you did set up DKIM, did you?). Just to name a few issues.
But even if implemented perfectly, there are a lot of 'enterprise' email 'solutions' out there that are not even close to implementing even the most basic of RFCs. Do not expect them to support punycode. Do not expect your emoji email to de deliverable to any of these services.