Hmm… Well, that only works for degrees in engineering, it’s a ‘Technical University’. Also, Delft is probably a great university, but it doesn’t strike me as more prestigious than the other Universities you mention.
For what it’s worth, the members of the Royal family all attended Leiden University. As did the current prime minister. Most ministers of justice in recent history attended Leiden University and were a member of Minerva, a conservative student society.
Still, I wouldn’t consider Leiden a particularly prestigious university—none of the Dutch universities are, because they are all relatively accessible and publicly funded. Instead, the well-connected manage to create their own little groups inside of student life. Like the aforementioned Minerva, which like other student societies (that exist in Delft as well), has students make small clusters (jaarclub, dispuut), with all kinds of barriers to entry. I presume the richest kids cluster together. People then rely on these connections throughout their career.
To me it sounds like you met a group of rich people who were friends in Delft University (and I presume already rich) and relied on this network afterwards: this is a pattern that reproduces itself at other Universities. And inversely, attending Delft University is by no means a guarantee that you can profit from this mechanism.
It’s interesting what you say of not seeing class differences before, I think it’s quite common in The Netherlands. The image the Dutch have of their society is one with very little class differences. This might be a comforting idea in day to day live (as you mention) but it also makes it hard to do something about the unfair situations that persist.