No.
The previous topic you cite was about situations where a pre-existing ability is temporarily ‘hidden’ by some other effect or status; this is the inverse, where an ability is
added temporarily, the effect ceases to exist, and then a different effect later grants it a similar-looking ability. It doesn't matter that the new ability looks the same as the old one–it's not the same as the old one.
To use the covering-up-text analogy from the previous question, when you use Mirage Mirror, you write down all of the target's characteristics onto a sticky note and cover the original card text with that paper, and when the effect expires, you remove the sticky note, light a match, and burn the note–it ceases to exist. If you activate the Mirror again at a later time, you need to write a completely new sticky note. Even if the words you end up writing on it are the same as the words you wrote last time, it's still a new note.