### Description

This is a followup to #85926.

As part of the ingest processing pipeline, we call `CollectionUtils.ensureNoSelfReferences(...)` to ensure that a script processor didn't accidentally introduce a circular object. However, this check is only necessary if we know there was the potential for a circular option, which can only happen with either a custom processor (a plugin where we have no control), or a script processor. We should be able to only call this sanity check if we know we need it, rather than for every document.
server/src/main/java/org/elasticsearch/ingest/IngestDocument.java
* @param path the path of the field to be removed
     * @throws IllegalArgumentException if the path is null, empty, invalid or if the field doesn't exist.
     */
    public void removeField(String path) {
        FieldPath fieldPath = new FieldPath(path);
        Object context = fieldPath.initialContext;
        for (int i = 0; i < fieldPath.pathElements.length - 1; i++) {
            ResolveResult result = resolve(fieldPath.pathElements[i], path, context);
            if (result.wasSuccessful) {
                context = result.resolvedObject;
            } else {
                throw new IllegalArgumentException(result.errorMessage);
            }
        }
        String leafKey = fieldPath.pathElements[fieldPath.pathElements.length - 1];
        if (context instanceof Map<?, ?> map) {
            if (map.containsKey(leafKey)) {
                map.remove(leafKey);
                return;
            }
            throw new IllegalArgumentException("field [" + leafKey + "] not present as part of path [" + path + "]");
        }
        if (context instanceof List<?> list) {
            int index;
            try {
                index = Integer.parseInt(leafKey);
            } catch (NumberFormatException e) {
                throw new IllegalArgumentException(
                    "[" + leafKey + "] is not an integer, cannot be used as an index as part of path [" + path + "]",
                    e