Is it possible for my team to use the DBMS_CLOUD PL/SQL package in a non-ADB database, on-premise or running over a VM in the cloud?
DBMS_CLOUD in PL/SQL Packages and Types Reference
Yes, this is now possible! You will need to manual install the DBMS_CLOUD package. The package is supported in Oracle Database 19c beginning with 19.9, as well as in Oracle Database 21c beginning with 21.3.
Here is the MOS note, updated by Oracle, to manually install the DBMS_CLOUD package on an Oracle database.