CREATE EXTENSION not adding extension on second SCHEMA

The following documentation comment has been logged on the website:

Page: https://www.postgresql.org/docs/14/sql-createextension.html
Description:

I'm trying to add an extension to two schemas that I have in my DB.

steps:

1)

CREATE EXTENSION unaccent with SCHEMA public;

response: OK.

2)

CREATE EXTENSION unaccent with SCHEMA public_test;

response: SQL Error [42710]: ERROR: extension "unaccent" already exists

I tryed:

SET search_path = public_test;
CREATE EXTENSION unaccent;

and the response is: response: SQL Error [42710]: ERROR: extension
"unaccent" already exists