plpgsql Extension not updating after replacing with updated sql & control files in postgres extension directory

Question

So I have a custom plpgsql extension that I installed in /usr/share/postgresql/13/extension that works properly.

The problem I'm facing is that I'm trying to update the extension by replacing the test_ext--1.0.sql & test_ext.control files with updated ones- test_ext--1.1.sql.

I've updated the control file to display version 1.1.

test_ext.control

# test_ext extension
comment = 'Test Extension for dummy_schema.'
default_version = '1.1'
relocatable = true
# requires = ‘pg_stat_statements’
# directory = 'extension'

My steps where:

1. drop the existing extension
2. replace .SQL & control files
3. CREATE EXTENSION test_ext SCHEMA dummy_schema;

After creating the extension, I'm still presented with the old extension rather than the new one.

                                        List of installed extensions
     Name     | Version |   Schema   |                             Description                              
--------------+---------+------------+----------------------------------------------------------------------
 test_ext     | 1.0     | dummy_schema        | Test Extension for dummy_schema.
 plpgsql      | 1.0     | pg_catalog          | PL/pgSQL procedural language
 postgres_fdw | 1.0     | dummy_schema        | foreign-data wrapper for remote PostgreSQL servers
 timescaledb  | 2.4.0   | dummy_schema        | Enables scalable inserts and complex queries for time-series data
(4 rows)

I've ran ALTER EXTENSION test_ext UPDATE to "1.1"; but I get an error saying

ERROR:  extension "test_ext" has no update path from version "1.0" to version "1.1"

I've even tried rebooting postgres service after extension install only to get same results.

I'm out of ideas.