One way to hold this word: a night sky opening up in light and noise, with somebody standing in the dark who planned every second of it. Two things are in that picture at once — the bright thing the crowd sees, and the careful craft behind it. Everything pyrotechnics means sits in one of those two places, and the figurative use simply lifts the whole picture off the sky and puts it on a stage.
From the word’s history
Wiktionary gives the word as pyro- + technic + -ics, with pyro- going back through Latin to Ancient Greek πῦρ (pûr), "fire". So the parts read as "the skills that have to do with fire", which is exactly where the craft sense sits, with the display being what that craft produces.
維基詞典把這個字拆成 pyro- 加 technic 加 -ics，而 pyro- 往上可以經拉丁文追到古希臘文的 πῦρ（火）。所以照字面拼起來就是「跟火有關的那些技術」。這正好落在「煙火製作」那個意思上，而一場煙火表演，就是這門技術做出來的東西。
Wiktionary entry for pyrotechnics, etymology tree (packet source_ref kaikki:3f6f69a190036ae4:779265805:23410)
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