why is the jump not replicated by default? Or is it?

Yes, (bPressedJump = true) and (Character->Jump()) do the same things…
They activate a physical impulse in the capsule (the jump itself).

But they say I should use Jump() function instead

Unfortunately it is not replicated… it’s a shame… I would like to expose this variable in the AnimBlueprint

I agree…
I was expecting the Jump() function to be in the character movement class…
However, it is in the character class. It’s a little confusing.

Thanks for your reply!!