(Potential spoilers) Question about BlazBlue series' play order

Greetings, everyone!

I finished BlazBlue: Continuum Shift Extended a few years back, but life happens and I couldn't play the rest of the series. Fast-forward to nowadays, and I decided to play the rest of the series, or, if anything, at least the main games. And reading on them, specially the one I played, since I remembered some quirks about it, I found a mention that apparently, part of its plotline is actually the plotline of Calamity Trigger, introduced in this edition. Is that correct? And if so, could I skip Calamity Trigger, or are there any benefits to playing it too?

Thanks in advance!