Think of the word as a small cloud that has to settle somewhere in the sentence. Put it next to the verb and it settles on the person doing the action: they speak, look or sit with that cloud over them. Move it to the front of the sentence and add a , and the cloud floats over the whole thing instead, so it is the writer who is sorry, not anyone in the story. Same word, same feeling; what changes is where it lands.
Our Wiktionary evidence gives unhappily as Middle English unhappily, equivalent to un- plus happily, or unhappy plus -ly. So the word is simply happily turned over, and nothing in the packet says more than that.
手上的 Wiktionary 資料說 unhappily 來自中古英語，等於 un-（不）加 happily，或是 unhappy 加 -ly。所以它就是把 happily 整個反過來。資料只說到這裡，再多的來源故事我們沒有依據。
Wiktionary via supplied kaikki extract 3f6f69a190036ae4, entry 'unhappily' (adv), etymology_text
Two branches
雲罩在動作上
這一支就是把雲停在動詞旁邊，交代做事時的心情。
r · B1
In a way that shows you are sad or not pleased. It can describe how someone speaks, looks or moves at one moment, and it can also describe living without happiness over a long time, as in 'unhappily married'.
不開心地、悶悶不樂地
雲罩在整句話上
同一片雲，往上升到句子外面，由說話的人來承擔這份遺憾。
r · C1
Used at the start of a sentence, with a comma after it, to show that you are sorry about the fact you are about to give and wish it were not true.
遺憾的是