oooff. No please don't let this become a norm. A few checkin emails? Sure. But given that offers can be pulled, each of those chats is going to feel like an interview to the candidate. Every call is likely to cause stress - and from the candidate's point of view, they can hardly refuse.
"The goal with these encounters is to keep people intelectually curious. Just share with them what's going well, and what challenges lie ahead. And maybe you can get them to brainstorm with you on some interesting issues."
No. They don't work for you yet, so stop trying to get them to do work for you. They probably have more than enough on their plate wrapping up work/doing handover at their old place. And they may want to actually take a break between jobs - not take a couple of unpaid weeks where you keep dragging them onto calls to do work.
If someone in effect started trying to onboard me and get me working on company problems before I'd actually started, THAT would be far more likely to make me run away than if I had total radio silence.