Jackson Databind Failing @JsonMerge with a custom Map with a @JsonCreator constructor

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Describe the bug

Continuation of https://github.com/FasterXML/jackson-databind/issues/4922.

Version Information

2.19.1, 2.19.2, 2.18.3

Reproduction

When the containing class of the Map is constructed with a @JsonCreator constructor, the issue comes back.

import java.util.HashMap;
import java.util.Map;

import com.fasterxml.jackson.annotation.JsonCreator;
import com.fasterxml.jackson.annotation.JsonMerge;
import com.fasterxml.jackson.core.JsonParser.Feature;
import com.fasterxml.jackson.databind.json.JsonMapper;
import com.fasterxml.jackson.module.paramnames.ParameterNamesModule;

interface MyMap<K, V> extends Map<K, V> {}

class MapImpl<K, V> extends HashMap<K, V> implements MyMap<K, V> {}

class MapUtils {

    static <K, V> MyMap<K, V> createMyMap() {
        return new MapImpl<K, V>();
    }
}

class MergeMap {

    @JsonCreator
    MergeMap(int inter, String s) {
        System.out.println("creator for " + map.getClass().getSimpleName());
        this.inter = inter;
        this.s = s;
    }

    int inter;
    String s;

    public int getInter() {
        return inter;
    }

//  public String getS() {
//      return s;
//  }

    @JsonMerge
    MyMap<Integer, String> map = MapUtils.createMyMap();

    public MyMap<Integer, String> getMap() {
        System.out.println("getMap");
        return map;
    }

    @Override
    public String toString() {
        return map.toString() + " " + inter + " " + s;
    }

    public static void main(String[] args) throws Exception {
        JsonMapper MAPPER = JsonMapper.builder()
                .addModule(new ParameterNamesModule())
                .configure(Feature.INCLUDE_SOURCE_IN_LOCATION, true)
                .build();

        var merge = new MergeMap(5, "f");
        merge.getMap().put(3, "ADS");
        System.out.println(merge);

        System.out.println(" == serializing --");

        var string = MAPPER.writerWithDefaultPrettyPrinter().writeValueAsString(merge);
        System.out.println(string);

        System.out.println(" == deserializing --");

        var merge2 = MAPPER.readValue(string, MergeMap.class);

        System.out.println(" == checking --");

        System.out.println(merge2);
    }
}

Gives

creator for MapImpl
getMap
{3=ADS} 5 f
 == serializing --
getMap
{
  "inter" : 5,
  "map" : {
    "3" : "ADS"
  }
}
 == deserializing --
Exception in thread "main" com.fasterxml.jackson.databind.exc.InvalidDefinitionException: Cannot construct instance of `example.MyMap` (no Creators, like default constructor, exist): no default constructor found
 at [Source: (String)"{
  "inter" : 5,
  "map" : {
    "3" : "ADS"
  }
}"; line: 3, column: 11] (through reference chain: example.MergeMap["map"])
    at com.fasterxml.jackson.databind.exc.InvalidDefinitionException.from(InvalidDefinitionException.java:67)
    at com.fasterxml.jackson.databind.DeserializationContext.reportBadDefinition(DeserializationContext.java:1915)
    at com.fasterxml.jackson.databind.DatabindContext.reportBadDefinition(DatabindContext.java:415)
    at com.fasterxml.jackson.databind.DeserializationContext.handleMissingInstantiator(DeserializationContext.java:1402)
    at com.fasterxml.jackson.databind.deser.std.MapDeserializer.deserialize(MapDeserializer.java:440)
    at com.fasterxml.jackson.databind.deser.std.MapDeserializer.deserialize(MapDeserializer.java:31)
    at com.fasterxml.jackson.databind.deser.SettableBeanProperty.deserialize(SettableBeanProperty.java:543)
    at com.fasterxml.jackson.databind.deser.BeanDeserializer._deserializeWithErrorWrapping(BeanDeserializer.java:587)
    at com.fasterxml.jackson.databind.deser.BeanDeserializer._deserializeUsingPropertyBased(BeanDeserializer.java:480)
    at com.fasterxml.jackson.databind.deser.BeanDeserializerBase.deserializeFromObjectUsingNonDefault(BeanDeserializerBase.java:1499)
    at com.fasterxml.jackson.databind.deser.BeanDeserializer.deserializeFromObject(BeanDeserializer.java:340)
    at com.fasterxml.jackson.databind.deser.BeanDeserializer.deserialize(BeanDeserializer.java:177)
    at com.fasterxml.jackson.databind.deser.DefaultDeserializationContext.readRootValue(DefaultDeserializationContext.java:342)
    at com.fasterxml.jackson.databind.ObjectMapper._readMapAndClose(ObjectMapper.java:4971)
    at com.fasterxml.jackson.databind.ObjectMapper.readValue(ObjectMapper.java:3887)
    at com.fasterxml.jackson.databind.ObjectMapper.readValue(ObjectMapper.java:3855)
    at example.MergeMap.main(MergeMap.java:74)

Uncommenting the getS() method resolves the issue, but shouldn't have affected the construction of the map. Also, declaring Map<Integer, String> map = MapUtils.createMyMap(); instead also works, but the whole point is to merge to an initialized custom type. It shows that the containing class construction is valid, however.