As verisimilitude drove soliloquies and choruses off the stage, what
device or character replaced them?

Some plays, such as Thornton Wilder's "Our Town," employ a character
who serves as a narrator.

well, i can't speak for the middle ages, but the device i can think of
after choruses is the monologue/soliliquay (with appologies for
spelling)

Plot (both real [on-stage] and imaginary [off-stage]).  For frame of
reference, read Aristotle Poetics and critism of both Shaw and Ibsen.