My wild fan theory: Somehow a Changeling of some kind has been living dormant inside of Jack Crusher and it's the key to establishing a new Great Link. Being in close proximity to other Changelings has begun to awaken it in Jack's psyche. We have never seen a changeling enter a solid's body, but given the way this is going and how they look different in the current iteration, I am guessing they can.
This explains Jack's visions without diminishing the impact of Picard having a real son.
Maybe we discover that Jack had heart surgery as a child, and a changeling (because reasons) decided to impersonate his donor heart?
Would work thematically, since it calls back to Picard's own artificial heart at least.