Question

I understand that your problem with the topic of prayer, and its implications for God's involvement in the world, stems first and foremost from a certain assumption: the Sages forbid praying about something that has already happened, because that is a "vain prayer." You tend to understand the term "vain" not as a halakhic prohibition, but as a factual assessment—meaning, such a prayer simply will not help. In other words, there is no normative prohibition here in the laws of prayer, but rather a statement that the Holy One, blessed be He, does not intervene in such cases.
Here I already want to comment on that assumption: after all, you yourself wrote that there is no doubt that the Holy One, blessed be He, can intervene in nature, since He created the laws of nature and can also freeze them or depart from them. In addition, you do not deny His miraculous intervention in the past, and you also do not deny sporadic intervention in the present.
So why not say this: technically, the Holy One, blessed be He, certainly can intervene, but in the matter of prayer there is a boundary that was set. That boundary is either halakhic-normative within the laws of prayer, or indeed it is possible to interpret the word "vain" more in your direction, as a factual statement—that the prayer simply will not help. But the intent would be: it will not help because the Sages understood theologically that the Holy One, blessed be He, perhaps will not want to intervene, or does not want people to turn to Him to intervene in nature in such a case. But surely one should not interpret "vain" as though the Holy One, blessed be He, generally cannot intervene, for we have already assumed that whoever created the laws of nature is also capable of changing them.
Once that assumption is accepted, the rest of the problems are no longer substantial. The Sages do indeed forbid praying for a miracle, and you are right that the deterministic reality of the laws of nature makes every intervention in nature, by definition, a miracle. At the same time, since the Holy One, blessed be He, has the ability to perform miracles and intervene in deterministic reality, the main issue is to define when He will do so and when He will not, and that is exactly what the Sages did: they set halakhic boundaries or stated theological insights as to when prayer can have an effect, because He may intervene and save. Regarding the matter of 40 days for the birth of a child—this is a boundary where, according to the Sages, there is room to pray, and after that there is not.
To explain the difference between before 40 days and after that, one can use the concept you brought in the laws of the Sabbath regarding a "pseudo-ontic doubt."
It was said in your lessons on the laws of the Sabbath that, seemingly, with a bench just as with a box of flies one can statistically calculate the probabilities of making a furrow, so why distinguish between them in terms of ontic doubt versus epistemic doubt? Rather, it must be said that with respect to a furrow, for an ordinary person, because of the complicated statistical calculations, it appears as though there is doubt, and therefore halakhically it is considered a "doubt in reality," and in your terminology, a "pseudo-ontic doubt."
Similarly, we can say here that before 40 days from the fertilization of the fetus (and in our scientific knowledge: the moment of fertilization), this is a situation that in reality supposedly cannot be seen except through complex statistical calculations—and therefore it is a "pseudo-ontic doubt" that allows prayer.
That is to say, the issue of when one may pray is a halakhic category that was set according to the human being (the Holy One, blessed be He, can in any case change nature), and this category was set according to his ability to discern, from his perspective, situations of a "gap" and doubt. And since from the perspective of a human being, who lacks the ability to do statistical calculations, there are still "several possibilities" here—he is permitted to pray. Even though essentially it is a miracle (which the Holy One, blessed be He, can perform).
After 40 days, the situation is perceived as certain, and therefore it is forbidden to pray.
Indeed, as you wrote, the difference between before 40 days and after is not a matter of a hidden miracle versus an open miracle, because the Sages did not have ultrasound, and even after 40 days, relative to sensory possibility—in their time—the matter was still considered "hidden."
But the category is not based on sensory observation; rather, it deals with what we "see" at the level of the intellectual knowledge available to us, regarding the moment when it shifts from a state of ontic doubt to a state of pseudo-ontic doubt.
In the time of the Sages, with the limits of their knowledge: 40 days for the fetus was the time when we moved from a state of pseudo-ontic doubt, because it was "clear" to us—according to the scientific knowledge that there are several possibilities—to a state of ontic doubt, where even in our eyes as human beings, reality had already been determined.
And in our time, the same idea applies, only in relation to the moment of fertilization.
A point that perhaps still needs to be resolved is why the Sages defined this as prayer for a "miracle," unlike before 40 days, when essentially that too is a miracle.
That is already a semantic question,
and perhaps, as was written, the concept of "miracle" with regard to prayer does not refer to the Holy One, blessed be He, and His abilities, because He can do anything, but rather to us—to define for us when, from our perspective as human beings, it is perceived as a change in nature. And that is in a reality of ontic doubt, after 40 days—and one may not pray. And before 40 days—one may.
Conclusion: every prayer is essentially a prayer for a miracle. The Holy One, blessed be He, can perform miracles. And He indeed does perform them. The Sages taught us that He performs them, or wants us to turn to Him to perform them in practice, only when in our case—as limited human beings—the situation appears as though it involves ambiguity (even though it does not, because everything is deterministic). That is, the Holy One, blessed be He, does intervene in the world; there is reason to turn to Him to change deterministic reality, albeit with certain qualifications.