The whole Commission has to be approved by the European Parliament, not just their President. The European Parliament has forced the European Council to remove candidates before approving the Commission multiple time in the past. In that sense the Commission is more directly elected by the people than e.g. German ministers (who can be chosen at will by the Chancellor).

And of course the national governments are elected (indirectly) by the people as well which makes everyone who they elect also indirectly elected (albeit through more indirection).

The EU commission is also indirectly elected by the people in a (maybe tenuous) way. Member state populations elect their national governments, those governments put forward commissioners. They're not that much different to civil servants in national government really.

We do not elect the national goverments. We elect political parties in the national parliament who then form a government or a coalition and appoint comissioners in the EC. There is in fact little representation.