Connect as postgres user on AWS RDS to install extension to pg_catalog
Your attempt to write to the pg_catalog schema probably fails because you don't have a superuser on RDS, just a role with limited admin privileges. And Amazon is smart enough to prevent users from messing with the system catalogs. I.e.: no CREATE privilege in the schema pg_catalog.
It's generally not advisable to install additional modules like citext into the pg_catalog system schema. (Some exceptions have the schema preset.) Install it to public or some dedicated schema.

Is it recommended to install extensions into pg_catalog schema?

The &quot;home&quot; schema of the installed extension needs to be in the search_path. The manual:

The schema containing the citext operators must be in the current
search_path (typically public); if it is not, the normal
case-sensitive text operators will be invoked instead.

You can easily set the search_path for one / some / all users or databases or user / database combinations or temporarily or for the current session or generally:

How does the search_path influence identifier resolution and the “current schema”