The cross-signature is expected to be issued by the “DST Root CA X3”, which is operated by IdenTrust.
You can find a copy of this CA root certificate at
https://ssl-tools.net/certificates/cv0tp9-dst-root-ca-x3
Hopefully that will help you figure out whether it’s accepted by the clients you’re wondering about. I don’t know the status of its inclusion in different versions of Java; I’d be glad to hear whatever you figure out.