Greek polemos is war, and this is the word that war left behind in a library. Picture someone who has stopped weighing both sides and started pressing one — attacking an idea, or standing over it to defend it. Nothing is hidden: the side is declared in the first line. The three uses are just that scene named three ways — the piece written, the skill of writing it, and the flavour it leaves on the page.
From French polemique, from Ancient Greek polemikos, of war, from polemos, war.
經法文 polémique 借自古希臘文 polemikós（與戰爭有關的），源頭是 pólemos（戰爭）。所以中文用「筆戰」來對，畫面幾乎是同一個。
packet Wiktionary etymology_text for polemic (kaikki:3f6f69a190036ae4:771465222:12768)
One branch
名詞：那一篇，和那門本事
同一場筆戰，一個是打出去的那一發，一個是打仗這件事本身。字典用可數與不可數把兩者分開。
noun · C1
A piece of writing or a speech that attacks an idea, an opinion, or a person very strongly — or defends one just as strongly. It argues one side hard and does not try to sound balanced.
論戰文章