In Japanese, mada まだ refers to a continuing state: 'still (as it was)' or 'not (changed) yet', and mou もう is about change: 'already (changed)' or 'no longer (the same)'. Are there other languages using a similar pair of words?
Yes, for example English as you pointed out in the question.
Or Norwegian: "ennå" and "allerede".
Or Dutch: "nog", and "al"
Or Czech: "ještě" and "již"
Or Mandarin: 還 and 已經
So basically it seems like all languages have ways to express these concepts.