Locking for update inside CTEs

If I make a query using CTEs that looks like that:

WITH cte_a AS (    SELECT a.id, a.something    FROM a    WHERE a.something IS NOT NULL ),-- [...] some other CTEscte_d AS (    SELECT         cte_a.id,        cte_a.something    FROM cte_a    JOIN         -- something    JOIN        -- something    WHERE         -- something    ORDER BY cte_a.id ASC    FOR UPDATE  -- Here, will the `FOR UPDATE` locks `a` rows?),-- rest of the query, which will update `a.something`.

Will the lock for update apply on the rows of the table a, or will the lock apply on a materialized table generated by cte_a?

If the lock applies to the materialized table, would the following solve the problem?

WITH cte_a AS NOT MATERIALIZED (-- Rest of the query

I'm using PostgreSQL v14.

If it changes anything, I'm mostly interested in the behavior with the default READ COMMITTED isolation level.