BUG #19051: Is it possible to move a TOAST table to a different tablespace than its parent table?

The following bug has been logged on the website:

Bug reference: 19051
Logged by: Mustafa HARARCI
Email address: mhararci@gmail.com
PostgreSQL version: 16.10
Operating system: Ubuntu 16.10-1.pgdg22.04+1
Description:

Hello everyone,

I'm currently using PostgreSQL 16.10 and I've run into a challenge regarding
moving TOAST data for a table. My goal is to have the TOAST data for a
column stored in a different tablespace from the parent table.

Specifically, I have a users table with a profile_data column of type JSONB,
which can contain large objects. I want the users table itself to reside in
the ts_medium_data tablespace, while its associated TOAST data is stored in
a separate ts_medium_toast tablespace.

I've attempted the following steps:

I created the users table in the ts_medium_data tablespace.

I identified the associated TOAST table using the pg_class catalog (SELECT
reltoastrelid::regclass FROM pg_class WHERE relname = 'users';), which
returned an object like pg_toast.pg_toast_16646.

As a superuser (postgres), I tried to move the TOAST table to the new
tablespace using ALTER TABLE pg_toast.pg_toast_16646 SET TABLESPACE
ts_medium_toast;.

This command, however, resulted in the following error: ERROR: permission
denied: "pg_toast_16646" is a system catalog.

This error suggests that direct modification of the TOAST table is not
allowed, even with superuser privileges.

My question is, is it fundamentally possible in PostgreSQL to store a
table's main data and its TOAST data in different tablespaces? Is this
behavior a design constraint? If so, is there any workaround for this, or is
this simply not a supported feature?

Any insight into this behavior or guidance on a potential solution would be
greatly appreciated.

Thank you.