Is there an arcade ladder or story of any kind for the new characters?

Title…

I want some context for the characters of S3. Is there any hint of lore or story in S3 right now?

No, it will come out at a later date, most likely when all characters of Season 3 have been released.
There will be a Shadow Lord mode as well which is a cool new Single player mode, but it is unknown when it will be out.