Yes, you can use the Cals and are backward compatable.
You can't use RDS CALs for earlier versions to access later versions of Windows Server, but you can use later versions of RDS CALs to access earlier versions of Windows Server. For example, an RDS 2016 CAL or higher is required to connect to a Windows Server 2016 RD Session Host, while an RDS 2012 CAL or higher is required to connect to a Windows Server 2012 R2 RD Session Host.
but it looks like you'll need 2022 session host
You must install your RDS CAL on a compatible RD license server. Any RDS license server can host licenses from all previous versions of Remote Desktop Services and the current version of Remote Desktop Services. For example, a Windows Server 2016 RDS license server can host licenses from all previous versions of RDS, while a Windows Server 2012 R2 RDS license server can only host licenses up to Windows Server 2012 R2.
https://learn.microsoft.com/en-us/windows-server/remote/remote-desktop-services/rds-client-access-license
--please don't forget to upvote
and Accept as answer
if the reply is helpful--