That's a great question and thanks for using QandA platform.
Yes, I think the .NET Core 3.1 is compatible with SQL Server 2022. Although .NET Core 3.1 is not the latest version of .NET Core, it should still work with SQL Server 2022. Microsoft ensures backward compatibility for older versions of .NET Core with newer versions of SQL Server to support a wide range of development scenarios and applications.
If this helps kindly accept the answer thanks much.