Salesforce Error 'API not enabled for this Organization or Partner'

Step 1: Check Your Salesforce Edition

API access is enabled by default for Enterprise, Unlimited, Performance, and Developer editions. Group, Essentials, and Professional edition orgs do not have API enabled by default. Professional edition customers can purchase API access as an add-on.
To find your Salesforce edition, follow the steps in: How to Find Your Salesforce Edition
If your org is on an edition that does not support API, contact Salesforce to discuss upgrading your edition or purchasing the API add-on (for Professional).

Step 2: Check the User Profile API Enabled Setting

If your org edition supports API, verify the API Enabled permission is enabled on the user's profile:

1. In Lightning Experience: Go to Setup > Users > Profiles. In Classic: Go to Setup > Administration Setup > Manage Users > Profiles.

Alternatively, find the user in the All Users list and select their Profile directly.

Step 2a: Classic Interface (Standard Profile Page)

Select the profile. Scroll down to Administrative Permissions. Enable API Enabled if it is not already checked.
 

Step 2b: Enhanced User Profile Interface

If using the Enhanced User Profile Interface, select the profile, scroll down, and select System Permissions. Enable API Enabled if it is not already selected.