Tableau Server 2019.2.3
On Tableau Server when changing the owner of a data source with embedded credentials it changes the connection type from "Embedded" to "Prompt User". Connection should retain the current settings of "Embedded".
See below screenshots to replicate
Existing Owner - connection set to "Embedded".
Using Tableau Server change the owner to Analytics user
Data source is now changed from "Embedded" to "Prompt User"