The vaccine’s matter is in your body for a day at most. The immune system is known for quite some time, and the immunization do happen. In what way could someone develop a side effect long after the vaccine? Of course medicine is data based, not necessarily about mechanisms, but at a point Occam’s razor has to apply. And either way, we would have seen by now any side effect since it has been injected into many millions for quite some time now.

Long-term effects are just that: long-term. We can't know what long-term effects the vaccines have until they have been used for a long time, even if millions have had them.