find_additional_properties in jsonschema/_utils.py collapses every patternProperties key into one regex with "|".join(...) and then guards it with if patterns:

patterns = "|".join(schema.get("patternProperties", {}))
for property in instance:
    if property not in properties:
        if patterns and re.search(patterns, property):
            continue
        yield property

"|".join maps both an empty patternProperties and {"": ...} to the same empty string, and if patterns then treats that empty (match-everything) pattern as absent. So an empty-string pattern key, which is a valid regex that matches every property, is silently dropped: its properties are reported as additional and validated against additionalProperties instead of the pattern subschema.

from jsonschema import Draft202012Validator as D

# "" matches every property, so patternProperties owns "x"; nothing is additional.
list(D({"additionalProperties": False,
        "patternProperties": {"": {"type": "integer"}}}).iter_errors({"x": 1}))
# before: ["'x' does not match any of the regexes: ''"]   (should be valid)

# The wrong subschema is applied, not just a spurious message:
list(D({"patternProperties": {"": {"type": "string"}},
        "additionalProperties": {"type": "integer"}}).iter_errors({"x": "hi"}))
# before: ["'hi' is not of type 'integer'"]   (should be valid: "x" matches "" -> string subschema)

The sibling helper find_evaluated_property_keys_by_schema (used for unevaluatedProperties) already iterates the patterns individually with re.search, so the two helpers disagree on the same schema. This change makes find_additional_properties do the same: iterate the patternProperties dict and skip a property if any pattern matches, which distinguishes "no patterns" (nothing to match) from an empty-string pattern (matches everything).

Added TestFindAdditionalProperties in jsonschema/tests/test_utils.py (fails before, passes after). The full JSON-Schema-Test-Suite still passes with no regressions.