Working:

http://localhost:8624/api/packages/my-debian/upload?purl=pkg%3Adeb%2Fnano%409.0-1%3Farch%3Di386%26distro%3Dwtf&distribution=x

Not working:

http://localhost:8624/api/packages/my-debian/upload?purl=pkg%3Adeb%2Fnano%409.0-1%3Farch%3Damd64%26distro%3Dwtf
Write-Error: Upload failed for pkg:deb/nano@9.0-1?arch=amd64&distro=wtf Distribution must be specified when adding a Debian package.

So the actual distribution doesn't matter since it's already part of the purl but upload fails when omitted.