Your post is confusing and has to less detailed informations
- Avoid the usage of ADO.NET provider in SSIS package, they don't proform well "by design". SSIS is written in unmanaged code, better use unmanaged data provider = OleDB/ODBC
- Select the right data provider. SSDT 2019 and older is 32 bit app and can utilize only 32 bit data provider
- ***"*I have to type both the server's name and the database name myself." To lazy to enter a name?