Think of a prince walking into a room. Everything around him is on a bigger scale than ordinary life — the house he lives in, the welcome he gets, the money in his hand. Princely can point at the prince himself (whose family, whose land, whose title), or at anything done on that scale. And because the scale is set so high, the word is easy to turn into a joke: put it in front of a very small number and the gap does the work.
From the word’s history
The supplied Wiktionary entry records princely as Middle English princely / pryncely, that is prince plus the adjective ending -ly, so the word literally says 'prince-like'. Every later use is still doing that: either belonging to a prince, or made to a prince's standard.
packet 裡的 Wiktionary 條目記錄 princely 來自中古英語的 princely／pryncely，也就是 prince 加上形容詞字尾 -ly，字面上就是「像王子那樣的」。今天不管是講歸屬還是講規格，其實都還在做同一件事。
Wiktionary, "princely"
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