Rocket Lab never wanted to do first stage recover on the Electron, but they later chose to and have succeeded in soft ocean landings under parachutes and will soon try and catch the parachutes with helicopters.
I fully expect they're are running the numbers on second stage reusability but unlike SpaceX [1] they don't tend to announce things until they are sure that's what they will pursue.
Rocket Lab only promised the Neutron will do 8,000kg to low-Earth orbit, and people are suggesting the rocket tanks can be stretched for added performance.
If SpaceX wasn't pursuing Starship they would continue to spend resources on second stage reusability for the Falcon 9. Even less than 2 years ago Elon Musk was still talking about using a ballute to recover the Falcon 9 second stage [1], but they later decided to put all their resources into the Starship.
But yeah 2024 far enough away that Starship (and New Glenn) should be operational by then, so the competitive landscape may be different. But that's all the more reason for Rocket Lab to pursue second stage reusability.