CREATE EXTENSION not adding extension on second SCHEMA

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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