To activate Wordpress API, please follow the steps below:
Login to your WordPress instance as an admin
Navigate to plugins (left menu) > Add New
Search for WordPress REST API Authentication plugin
Click on Install Now and once installed, click on Activate

Configure REST API Basic Auth using UserName & Password:
In the plugin, go to the Configure API Authentication and click on Basic Authentication
Select the Username: Password as the Basic Authentication Key Type and click Save Configuration
Use your login username and password to connect

Please find below a reference to REST API documentation
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