@Sharon Tamm - Thanks for the question and using MS Q&A platform.
It seems like you are encountering an error while setting up a scan on an on-prem database/server in Microsoft Purview. The error message you are seeing indicates that there is a login failure due to an untrusted domain.
Based on the information you provided, it seems like the domain service account you are using to connect to the database has the correct permissioning within Purview and has db_reader access to the intended database. Additionally, the server is running in mixed mode, so there should be no issues there.
One thing you may want to check is whether the domain service account is actually in the same domain as the database/server you are trying to scan. If they are not in the same domain, this could be causing the login failure.
Another thing you can try is to check the firewall settings on the database/server to ensure that the necessary ports are open for communication with Purview. You may also want to check the networking requirements for self-hosted integration runtimes.
For more details, refer to Connect to and manage an on-premises SQL server instance in Microsoft Purview
If you are still having trouble, you may want to open a support for further assistance.
Hope this helps. Do let us know if you any further queries.