There is a lot of backstory that doesn’t belong in your script. It feels important to put on the page, to explain things and illuminate characters, but it’s more interesting to the reader NOT to know everything, to guess and speculate and draw our own conclusions.
Bonus points if we get it wrong and that’s revealed later.
The most readable screenplays deal with now problems. Oversharing backstory slows everything down. Look for it when your characters stop to reminisce.
Of course, there is some backstory you can’t live without.
To put linchpin backstory in, give it a point of view. Deliver it with a threat, in a shroud of secrecy, as a warning, as an embarrassing put down or a big reveal in an emotional moment of confrontation.