And what would happen next to ensure that von der Leyen was removed from office?

It is worth remembering at this point how von der Leyen first became Commission President. She was controversially nominated by the European Council - who are not directly elected representatives within the EU system - deviating from the spitzenkandidat convention in a way that surprised and angered many MEPs - who are. Her own national government (Germany) did not support her in the Council voting because one of the parties in the governing coalition opposed her. She was eventually confirmed by a narrow majority in a secret ballot of the European Parliament from which little can therefore be determined about who did or didn't vote for her except that quite a lot of MEPs who were expected to support her candidacy based on public statements did not in fact do so in the secret vote.

So she was essentially proposed by a group of people who aren't directly elected at EU level and in some cases aren't even directly elected by the nations they represent - in violation of the normal convention expected by the only people who are directly elected at EU level - and was then narrowly confirmed by that directly elected group only in a secret ballot from which the vote of each individual representative was not recorded and there is therefore no possibility for their own electorates to hold those representatives to account personally for how they voted. Given that we are talking about the most influential political post in the EU this is not exactly a powerful demonstration of democratic legitimacy and a clear popular mandate no matter how you look at it.