All of the why questions were answered in MoS. Jonathan spoke about one day when Clark would see his differences as a blessing. Clark talks about wanting his life to have purpose. A blessing is something that is perceived of as a gift. The idea is that Clark's differences, his powers, are a gift he can give in the service of others. It's the "reason" that he was sent to Earth, as Jonathan hints at when he's a teenager and Jor-El confirms when he's an adult. In BvS, we get more of a sense of this when Clark worries that his gifts are no longer that blessing. That dream doesn't seem real anymore when people die in the Capitol bombing because of his presence there; so he wonders if he's doing more harm than good.
Even Clark's conversation with Jonathan focuses on the why of it all. Specifically, why continue to do good if you don't get the results you want? This is the heart of Superman's existential arc in this film filled with existential arcs. Does one do good to receive the "hero cake," as Jonathan did as a child, or does one do it even though it can mean carrying the burden of the nightmares of all the things one can't control or fix? In choosing to embrace his mission as Superman following this test, Superman affirms his purpose.
It's not implied that it's something programmed into him any more than it is for Reeve Superman; although with him his journey and motivations are even more opaque given the narrative cheat of the Fortress transformation. Clark is raised by kind and loving parents whose own choice to adopt him exemplifies grace: instead of being afraid, they chose to view this strange baby that fell from the sky as a blessing. They, in turn, raise him to make sense of his differences and cope with them by framing them as follows:
One day you're going to think of [these changes you're going through] as a blessing. [...] Somewhere out there you've got another father too, who gave you another name. And he sent you here for a reason, Clark. And even if it takes you the rest of your life, you owe it to yourself to find out what that reason is.
In other words, doing good for the world gives not only Clark's differences, his powers, meaning, but it gives his whole existence meaning. Speaking to Jor-El, as Jonathan predicted, only clarified the specific dreams and goals his biological parents had, but from an early age Clark was taught, as many Christians and likely people of other faiths are also taught, that whatever god they pray to created them with a purpose. Clark begins to want to seek his purpose as a teenager: "I'm tired of safe. I just want to do something useful with my life."
I highly recommend reading Mark Waid's essay
"The Real Truth about Superman: And the Rest of Us Too" because it aligns almost perfectly with what I and the films have expressed about Superman's motivations. Here's an example. After years of loving and working on the character, Waid writes that "the one question I could not answer [was] why does [Superman] do what he does?" The essay follows several of his trains of thought, but he ultimately concludes "When [Superman] lives as who he really is, in full authenticity to his nature and gifts, and then brings his distinctive strengths into the service of others, he takes his rightful place in the larger community, in which he now genuinely belongs and can feel fulfilled. [...] In helping others, Superman helps himself. In helping himself, he helps others." He adds, "Kal-El knows instinctively that it is only when he puts his gifts to use that he truly feels alive and engaged."
It was, Derek, hence the whole "Must there be a Superman?" question that Clark is forced to reckon with in the face of the existential threat that all of the controversy and specifically the carnage of the Capitol created. The movie doesn't suggest it's Lois and Martha, especially Martha. The Lois idea I can kind of understand, because of the "You are my world" thing, but Martha is not a part of that. As for the Lois aspect, all that means is Lois gives Clark faith that there is good in the world. She's his Superman. Again, it's a way to make or reconcile the general and the specific, the macro and the micro, the abstract and the concrete.