You can think of propriety as what belongs to a situation. Every room comes with things that are its own — a voice, a distance, a way of sitting — and propriety is the sense of what this room has been given. Behaving with propriety is handing the room back what is properly its own.
Propriety is a doublet of property: both come from Latin proprietas, what is one's own. In late Middle English it still meant ownership. The step from what belongs to a person to what belongs to a situation is what gives us the modern meaning.
propriety 和 property（財產）是同一個字的兩個分身，都來自拉丁文 proprietās（屬於自己的東西）。中古英文晚期它的意思還是「所有權」。從「屬於某人的東西」走到「屬於這個場合的東西」，就是今天「得體」這個意思的來路。Wiktionary 也把它拆成 prop(e)r + -iety，所以它跟 proper 是一家人。
Wiktionary entry for propriety, etymology section (packet source_ref kaikki:3f6f69a190036ae4:789853063:30241)
One branch
屬於這個場合的樣子
單數講的是那份分寸本身，複數講的是分寸拆開來的那些條目。
noun · C1
The quality of being right and suitable for the situation, judged by the rules of good behaviour that the people around you accept. It is also used when people ask whether an action was a proper thing to do at all.
得體；妥當