The European Council does nominate the candidate and infamously in 2019 overrode the informally agreed on spitzenkandidaten process, by which the nominee of the political group (EU Parliament equivalent of parties) with the most seats should have gotten the nomination.
That said, the EU Parliament is not bound by the nomination. It can very obviously reject any candidate it doesn't like, though of course the dynamics of candidate selection are heavily influenced by the European Council's nomination power.
But yes, there's nothing per se undemocratic about it and I'm a bit bewildered by people asking for direct election of the President rather than cleaning up the existing process, given that most EU member states elect their heads of government indirectly.