I am not sure so replanning prepared plans due change of search_path is expected in all use cases. Minimally it should be mentioned as possible incompatibility.
Use case - move record from schema A to schema B with prepared statements
SET search_path = 'A';
PREPARE x(int) AS DELETE FROM tab WHERE id = $1 RETURNING *;
SET search_path = 'B';
PREPARE y(int, int) AS INSERT INTO tab VALUES($1, $2);