https://www.thefreedictionary.com/turn+of+phrase

Почему-то в русском "Емкая фраза в соцсетях" = статус (!)

Опаньки! Не знала)

quip - is it an extra meaning to https://www.lingvolive.com/ru-ru/translate/en-ru/quip ?

A quip is a short comment, usually humorous, seen in chats, social media, captions, etc.

that was my point
"ёмкая фраза" вовсе не обязательно humorous, я бы даже сказал скорее всего, не humorous

It’s not always humorous in English either, it can be sarcastic, critical, as long as it’s succinct.

OK

When it’s sarcastic or snippy, it’s also called a WISECRACK