Can the 'returning' clause return source columns that are not inserted?

Question

Here's a minimal example of my real-world problem:

create table t(id serial primary key, rnd double precision);

of course you can return the inserted columns with a returning clause:

with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *;
/*
| ID |            RND |
|----|----------------|
|  9 | 0.203221440315 |
*/

you can also return a literal:

with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *, 1.0 dummy;
/*
| ID |            RND | DUMMY |
|----|----------------|-------|
| 11 | 0.594980469905 |     1 |
*/

but you can't return the source columns:

with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *, w.rnd;
/*
ERROR: missing FROM-clause entry for table "w": with w as (insert into t(rnd) values(random()) returning *) insert into t(rnd) select random() from w returning *, w.rnd
*/

Is there any way I can get w.rnd out of the final returning clause?

db<>fiddle here