X.400 is still in use today for things like sending invoices and orders through EDI.

Yes, it is a pain to manage. Yes, it is all still mostly running on 20+-year-old hardware and software.

It is slightly ironic that the main way we communicate X.400 addresses between parties is through modern email.

Is that actually true today? When I was doing EDI stuff ~20 years ago, it was mostly done using FTP, with some forward-thinking orgs moving to SFTP or (HTTPS-based) AS2.

I see that Wikipedia claims that "X.400 is quite widely implemented[citation needed], especially for EDI services", and that might once have been the case - but I doubt it was particularly widespread even at the time that article was first written. It's worth noting that that [citation needed] tag dates from October 2008!