"The new Minimum Access - API Only Integrations user profile is used with the Salesforce Integration user license to provide the minimum required access to API users. The Salesforce API Only Systems Integration user profile currently in use incorrectly provides CRUD permissions to custom objects. Replace with the new Minimum Access - API Only Integrations user profile."
So, what went wrong here?
Is making this switch as painless as indicated in the release notes? We just need to update the profile, and nothing else?
Mohit Kumar Agarwal (Dell Technologies) 
Forum Ambassador
This is only applicable to new org
Beginning with the Spring ‘24 release, the Salesforce API Only Systems Integration user profile isn’t available in newly provisioned Salesforce orgs.
The new profile is based on the existing Minimum Access - Salesforce Profile and provides the API Enabled and Api Only User permissions. Further permissions can be seamlessly added through permission sets and permission set groups.
See this also - https://developer.salesforce.com/blogs/2024/02/invoke-rest-apis-with-the-salesforce-integration-user-and-oauth-client-credentials
