Validate Nested JSON Configurations

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Problem

Given a JSON string representing a hierarchical model configuration, parse it and validate every nested object. Each node must contain a string field name, a string field type, an object field params, and an optional array field children. Return a list of validation errors using dot-paths such as children[1].params.lr. If the JSON is invalid, return [{"path": "$", "message": "invalid json"}].

Constraints

1 <= len(payload) <= 10^5
Maximum nesting depth is at most 10^3
Each node contains only valid JSON value types
children, when present, must be an array of objects

Function Signature

def validate_model_config(payload):

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