MonoBehaviourとの兼ね合いを考えるのが面倒になったので、asmdefでNoEngineReferencesにチェックが入ってるやつだけnull許容参照型を有効にするという妥協をしたバージョン

EnableNullable.cs

using System;
using System.IO;
using System.Linq;
using System.Xml.Linq;
using UnityEditor;
using UnityEditor.Compilation;
using UnityEditor.Experimental;
using UnityEditorInternal;
using UnityEngine;

public class EnableNullable : AssetPostprocessor
{
    private static string OnGeneratedCSProject(string path, string content)
    {
        var assemblyName = Path.GetFileNameWithoutExtension(path);
        var assemblyDefinitionFilePath = CompilationPipeline.GetAssemblyDefinitionFilePathFromAssemblyName(assemblyName);
        if (string.IsNullOrWhiteSpace(assemblyDefinitionFilePath)) return content;

        var assemblyDefinition = EditorResources.Load<AssemblyDefinitionAsset>(assemblyDefinitionFilePath);
        if (!assemblyDefinition.text.Contains("\"noEngineReferences\": true")) return content;

        var document = XDocument.Parse(content);
        if (document.Root == null) throw new Exception($"document.Root == null");

        XNamespace xNamespace = "http://schemas.microsoft.com/developer/msbuild/2003";

        // ReSharper disable once PossibleNullReferenceException
        var propertyGroup = document
            .Element(xNamespace + "Project")
            .Elements(xNamespace + "PropertyGroup")
            .First();
        propertyGroup.Add(new XElement(xNamespace + "Nullable", "enable"));
        return document.ToString();
    }
}