Do cases of scientific foreknowledge in the Bible come from Exegesis or Eisegesis?

No. It's not science - go speak to a scientist to find out. Or better still, actually study some science.

If a text mentions a tree am I suddenly a botanist?

The Bible mentions what it does because it is also about the world. Because humans live in a world and its presenting a certain cosmogony about the relationship of humans to the world around them.

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@curiousdanii: Whilst God knows more about trees than we will ever do; reading the Bible doesn't make us into God - to think so is, in the Christian dispensation - blasphemy. Which is why we still have to study trees and much else to become a botanist. So what's your point?

As Galileo once famously said,

the Bible tells you how to go to heaven, not how the heavens go.

The cases you mention require a rather liberal interpretation of the text, and for some it would be quite a stretch to assume that bronze age humans would be able to interpret these as Christians do today, as they were unaware of phenomena like entropy and thermodynamics.

Isaiah 45:12, 40:22, 42:5; Job 9:8; Psalms 104:2

The Hebrew שָׁמָ֑יִם (šā·mā·yim) generally means "heaven" or "sky", not "universe". The Hebrew word is constructed of two parts: sham (שָׁמַ) derived from Akkadian samu meaning "sky" or "lofty", and Hebrew mayim (מַיִם) meaning "water". It is a reference to clouds (the water) in the sky, not the universe. We know this because the sun is called shemesh. It follows the same construction, where shem or sham (Akkadian: samu) means "sky" and esh (Akkadian: ish) means "fire", i.e., "sky-fire".

It also contradicts Genesis 1:6-8, in which The "firmament" is claimed to be a solid "roof" over the world.

We should also mention that according to Genesis, the Earth & sky were formed before the Sun. Aside from bio-mechanical problems, this flatly contradicts the nebular hypothesis of stellar formation, in which planets form in the accretion disk created by a young star.

Job 38:31-32

Can you fasten the chains of the Pleiades or loosen the belt of Orion? Can you bring out the constellations  in  their  season and lead the Bear  and  her  cubs? 

This is not a correct description of the stars - it just alludes to constellations, patterns humans see where there are just random star positions. Furthermore, the Bible also incorrectly defines stars as objects that fall from heaven:

And the third angel sounded, and there fell a great star from heaven, burning as it were a lamp, and it fell upon the third part of the rivers, and upon the fountains of waters - Revelation 8:10

Job 26:7

during all days of the earth, seed-time and harvest, and cold and heat, and summer and winter, and day and night, do not cease

There is no indication here that the earth is "round" (it is actually spherical). The seasonal facts stated here are not foreknowledge, but demonstrably based on the experience of previous generations from before mankind became sedentary.

Psalms 8:8

Bird of the heavens, and fish of the sea, Passing through the paths of the seas!

This is not what scientists would describe as the water cycle.

Genesis 2:1 & Psalms 102:25-26

And the heavens and the earth are completed, and all their host;

Beforetime the earth Thou didst found, And the work of Thy hands are the heavens. They -- They perish, and Thou remainest, And all of them as a garment become old, As clothing Thou changest them, And they are changed.

This is a classical misapplication of the 1st and 2nd Law Of Thermodynamics, which refer to closed systems. Our planet is an open system constantly receiving thermodynamic energy from an external source. The Earth is definitely not a closed system: the planet loses about 50.000 metric tons of its atmosphere each year.

Do cases of scientific foreknowledge in the Bible come from Exegesis or Eisegesis?

Most cases of course are from eisegesis. People read about some scientifically determined fact, read some scripture that supports it, and then claim that the scripture predicted the fact. Those that like to tout Nostradamus by relating his cryptic writings to events in the news, rather than by using his writings to predict things that will soon appear in the news.

If a case were truly a result of exegesis, people would have read the scripture, extracted the fact, and recorded this fact as revealed knowledge, and then, long after that, science would have determined that yes, that fact is actually true.

There is one example I can think of. I wrote (in February 2020, before the relationship between bats and COVID-19 was known) about it on a different site:

… the laws of hygiene and nutrition were thousands of years ahead of science.

Practices such as cleanliness, quarantine, and avoiding sick people and corpses and isolating oneself when unavoidable, ensured much better general health. During the Black Plague for example, Jewish communities fared far better than the rest of Europe, precisely because of their following Biblical health rules.

There are many possible reasons why Jews were accused to be the cause for the plague. … Additionally, there are many Jewish laws that promote cleanliness: a Jew must wash his or her hands before eating bread and after using the bathroom, it was customary for Jews to bathe once a week before the Sabbath, a corpse must be washed before burial, and so on. — Jewish persecutions during the Black Death - Wikipedia

And, if the world followed the kosher laws, the influenza epidemics over the last 150 years would probably not have occurred. They almost all originated in China under conditions where ducks and swine are raised together. Ducks can catch viruses from wild birds (mostly harmless), and people can catch viruses from swine (mostly harmless), but conditions where ducks and swine live in each other's filth allow duck and swine viruses to exchange genes (extremely rare events), resulting in these sudden outbreaks where wild bird viruses are quite harmful to humans (e.g. the current Covid-19 situation).

Similarly, other outbreaks also result from non-kosher practices, such as ebola from eating bats:

It is thought that fruit bats of the Pteropodidae family are natural Ebola virus hosts. Ebola is introduced into the human population through close contact with the blood, secretions, organs or other bodily fluids of infected animals such as fruit bats … — WHO: Ebola virus disease

and AIDS from chimpanzees:

Scientists have traced the origin of HIV back to chimpanzees and simian immunodeficiency virus (SIV), an HIV-like virus that attacks the immune system of monkeys and apes. — History of AIDS

A remarkable quality of biblical language is that whatever century you find yourself living in, biblical points about the natural world remain valid. Given the ancient dates for the scriptures, it comes as no surprise to anybody, at any time, that we never see words like 'planets' or 'science' because those were words coined in the 19th century. That is why we don't have the Genesis creation account saying God "also made the stars and the planets". It stops after 'stars' because that was the only word available to describe what humans could see in the night sky with their naked eyes.

However, there are some statements about planet earth and the heavenly bodies that now seem to be astonishingly in harmony with modern scientific theories. For example, compare these prophesies (still to be fulfilled) with what scientists think will happen in the future:

Joel 2:10 Isaiah 2:19 & 13:6-10 & 24:19-23 & 34:1-4 Nahum 1:5 Matthew 24:29-30 Hebrews 1:10-11 & 12:26 2 Peter 3:7-12 Revelation 6:12-14 & 8:5 & 16:17-21

Science estimates that the sun will run out of fuel in about 4.5 billion years’ time. It’s now about halfway through its solar life. The end will see the sun expand to engulf Mercury and Venus. Earth will be turned to a cinder at that point. After the sun expanded, its explosion would then cause it to collapse into a black dwarf. (It would be too small to turn into a black hole.) End of all life in our solar system, no matter what. It’s only a matter of time. But the explosion of the sun fits in astonishingly well with the biblical prophecy in 2 Peter chapter 3, and elsewhere in the Bible.

Now, nobody ever thought of those biblical prophesies in terms of scientific theories for the 'death' of our universe until after those theories were formulated (comparatively recently). But, with hindsight, it could be seen that apparently ridiculous, unbelievable future descriptions in the Bible might not be so ridiculous or unbelievable after all.

But it's a mistake to call such biblical passages "scientific foreknowledge". God's foreknowledge is at work in the Bible, even though we might take a few thousand years to see it in a clearer, more scientifically explainable light. We are all trying to do catch-up, you see - Bible-believers and scientists alike. We are behind with our understanding and need to expand it. And that applies equally to Bible-believers as it does to scientists. Everyone needs to be open to facts, and then to think very carefully about how best to interpret those facts in light of what the ancient scriptures said, and what science is still discovering. We are all on a huge learning curve and nobody should be so proud that they ridicule either of those two branches of discovery.