Although not announced for iOS 16.3, there is more Apple Music Classical code within the beta release, and it's being changed as the service gets closer.
Apple's recent developer beta of iOS 16.3 was a release candidate, and it's expected to be issued publicly in the next week. There is no sign that the delayed Apple Music Classical will be included, but there is sign that the service continues to be worked on.
It's not correct that the service was only just now named Apple Music Classical, as beta iOS code in September 2022 called it that too. But the code is changing between betas, which means it's still being worked on.
Apple has not commented on these code fragments, nor about its previous commitment to launch by the end of 2022. It made that commitment in August 2021, when Apple bought the Primephonic classical music streaming service.