Why am I seeing an API response indicating 'too many items in operation'?

Environment:

Public APIs (Connect REST, Connect Web Services for SOAP)
All product versions

Issue:

We are seeing an API response stating:

Too many items in operation - exceeds internal limit of 1000 items per operation

Resolution:

The reason for this error response on public API requests is due to a limit being reached in terms of the amount of objects sent in a single Batch request. The Batch operation enforces a hard limit of 100 items, as well as the limit of 1,000 objects on each CRUD (create, update or delete) operation.

For further details on this topic see Answer ID 8264: Optimal efficiency when creating or updating objects using CWS API.