Faith is required, if for nothing else, to overcome solipsism. You confirm this yourself when you state, without equivocation, that reality has priority over consciousness. I note that you don’t distinguish between internal and external reality, but I assume you mean the latter? A Monist would argue that they are inseparable, but that is another question really.
I disagree that solipsism is relevant here.
At the very least, I can conclude through inductive reasoning that the self-consistent "world" which I perceive with my senses is not one that I have control over, and so it still makes sense to refer to it as "external" even under metaphysical solipsism.
When you accept that there is this world outside of your control, you can use observation to gain data about this external world and logically analyze that data. That's how I came to conclude that the natural world predates my existence and that my experience of it is merely an abstraction of the biological signals in my nervous system.
Whether you accept solipsism or, as I do, naturalism, the methodology is the same and so is the conclusion.
Anyway, in dismissing as magical thinking the uncomfortable idea that consciousness, however we define it, may come before reality, you are making a leap of faith; you trust in the existence of a world independent of your perception of it. And you trust, it seems, in logic and reason to help you under something of that reality. It is but a small step from faith in logic and reason,
I trust in logic, but I don't have faith in it. Logic is a self-correcting mechanism, so it is constantly questioning and re-evaluating its own conclusions in the face of new premises and counter-arguments.
I think faith in logic would probably look more like the verificationism of Logical Positivism, which I do not ascribe to.
It is but a small step from faith in logic and reason, to faith in the proposition that we are each part of something far greater than ourselves, and that some great and incomprehensible (to us) purpose underlies all.
You could describe us as all as being a part of something far greater than ourselves, but logic can't get you there alone because "greater" is an evaluative claim, not a factual one. Logic is limited in the sense that it cannot bridge the gap between facts and values.
It can judge whether something meets a given set of criteria or deductively follows from a given set of assumed premises, which we see in axiology as applied in mathematics, statistics, ethics, aesthetics, etc. However, those axioms do not derive from logic.
I do find value and meaning in logic. That said, finding meaning in logic seems to me to have very little to do with having faith in anything, especially that there is a great and incomprehensible purpose that underlies all. I actually think the proper application of logic is outright at odds with faith, and the two are completely opposed methodologies, since most forms of faith that I've seen espoused are considered some form of logical fallacy.
The only exception to that, which I've seen in common use, is when faith is used synonymously with trust. If that's the sense you mean by faith, then you're probably correct: the majority of people have some degree of trust in something. I just don't see how you're getting from that to believing in God.