DictStringInt.cs

using Godot;
using System.Linq;

[Tool]
public partial class DictStringInt : Node3D
{
	private System.Collections.Generic.Dictionary<string, int> _data = new();
	
	private void OneSecTick()
	{
		GD.Print($"_data: {string.Join(", ", _data.Select(it => $"{it.Key}: {it.Value}"))}");
	}

	public override Godot.Collections.Array<Godot.Collections.Dictionary> _GetPropertyList()
	{
		var properties = new Godot.Collections.Array<Godot.Collections.Dictionary>();
		properties.Add(new Godot.Collections.Dictionary()
		{
			{ "name", "MyCustomData" },
			{ "type", (int)Variant.Type.Dictionary },
		});

		return properties;
	}

	public override Variant _Get(StringName property)
	{
		if (property == "MyCustomData")
		{
			var value = new Godot.Collections.Dictionary();
			foreach (var pair in _data)
			{
				value[Variant.From(pair.Key)] = Variant.From(pair.Value);
			}
			return value;
		}
		return base._Get(property);
	}

	public override bool _Set(StringName property, Variant value)
	{
		if (property == "MyCustomData")
		{
			var dict = value.AsGodotDictionary();
			_data.Clear();
			foreach (var pair in dict)
			{
				_data[pair.Key.AsString()] = pair.Value.AsInt32();
			}
			return true;
		}
		return base._Set(property, value);
	}
}

DictStringIntDemo.tscn

[gd_scene load_steps=2 format=3 uid="uid://1v34fimr1fby"]

[ext_resource type="Script" path="res://DictStringInt.cs" id="1_poo7v"]

[node name="Node3D" type="Node3D"]
script = ExtResource("1_poo7v")
MyCustomData = {
"abc": 123
}

[node name="Timer" type="Timer" parent="."]
autostart = true

[connection signal="timeout" from="Timer" to="." method="OneSecTick"]