For your examples you could craft a routine to tell you this informationanything ending in a gdb will be file geodatabasedo a describe on a sde connection and look at the instance will tell you that database it is based on the connection string e.g.
desc = arcpy.Describe(Database Connections\Localhost SQL.sde)
cp = desc.connectionProperties
The only issue I see are the old style SDE connection where the instance will be a port number.
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