I wouldn't say entirely. Starship isn't going to be involved in Artemis II, but Artemis III supposed to take humans to the moon in December 2025. Nobody's on schedule.
No SLS II isn't ready now. Its launching mid next year, but there are concerns about Orion's heat shield. Also, II isn't planned to land on the moon. And it may be delayed further.
Artemis II is entirely delayed by Lockheed’s Orion spacecraft. Not SpaceX’s Starship.