Are non-used CTEs never materialized in PostgreSQL 16?

I want to return my post rows in one of three sort orders, controlled by a sorting_param function parameter. The sorting is complex, doesn't lend itself to a simple ORDER BY CASE .... So I'm thinking of writing each sorting into its own CTE, and then picking one of the CTEs as the final output. However, I wouldn't want PostgreSQL to waste time on all three, just the one I selected. So will all three be materialized or only the one I picked? Or is there a better way to do this? PostgreSQL version 16. Simplified code below.

WITH posts_by_order1 AS(    SELECT p.id    FROM post p    ORDER BY [some complex ordering 1]    LIMIT 10),posts_by_order2 AS(    SELECT p.id    FROM post p    ORDER BY [some complex ordering 2]    LIMIT 10),posts_by_order3 AS(    SELECT p.id    FROM post p    ORDER BY [some complex ordering 3]    LIMIT 10)SELECT * FROM posts_by_order1 WHERE sorting_param = 0UNION ALLSELECT * FROM posts_by_order2 WHERE sorting_param = 1UNION ALLSELECT * FROM posts_by_order3 WHERE sorting_param = 2;

Unfortunately I can't do this:

    ORDER BY         CASE             WHEN sorting_param = 0 THEN p.date             WHEN sorting_param = 1 THEN p.name             ELSE NULL         END DESC, ...