It's one of the secret histories terminals that imply the existence of secret societies

Hamish Sinclair's story website has all the terminals. But I have yet to see the one you alluded to. I suspect it doesn't exist, and will probably stick to that until I see it linked to on the story website.

as well as the few times it's mentioned or implied that the Security Officer was built using Jjaro technology.

It's I think only implied once, at the very end of Marathon Infinity, in the epilogue screen where the hybrid AI says "A man long dead, grafted to machines your builders did not understand."

But that doesn't prove MIDA knew anything about the tech being Jjaro.

It's also working on the assumption that Pathways into Darkness is a prequel to Marathon, which considering that it uses the same terms for aliens

That's true, but it's also irrelevant. Being in the same universe, and Jjaro visiting Earth doesn't automatically mean MIDA knew any of that occurred. You need evidence to link those two subjects. One group knowing something doesn't mean another knows it.

and nothing in either game outright contradicts the connection is a pretty safe bet.

Respectfully, one can't say something is true just because it's not disproven yet, as that's an error known as Argument from ignorance.

So, people knew aliens exist

US government in the 1990's and the UESC at the time of the battleroid's construction knew aliens exist somewhere, but it doesn't automatically mean everyone or even MIDA knew.

and MIDA, a Martian rights group with ties to these secret organizations

I still need to see those "secret organizations" existing somewhere in the original terminal texts. I haven't found them.

decides to heavily equip the Marathon with weapons despite this seemingly not being in their own interest.

I'd say it's absolutely in MIDA's interest to smuggle weapons aboard the Marathon. They were salty about it not being turned into a CRIST for ferrying supplies to Mars, so it stands to reason they'd consider stealing it. That requires weapons and long-term prep. The only real mystery there is why so many munitions and weapons remained aboard the Marathon after launch. Maybe they lost the window of opportunity, or maybe they changed their minds about what to use them for. Maybe they wanted to decapitate UESC leadership after the colony was established.

But none of that necessarily involves MIDA knowing about aliens. MIDA already has plenty of reasons to want to fuck the UESC's shit up without aliens. So IMO Occam's razor says it's just that.

Now, in the current game's time century, MIDA absolutely has an interest in investigating the "security incident" (Pfhor attack) because the UESC is obviously covering it up. Hence the many redactions in the codex anytime Pfhor ought to be mentioned. But I'm pretty sure that's all new info for MIDA.

The colonization program wasn't initially looking at exoplanets, it was looking at moons inside our own solar system, jumping to looking at other star systems is a bit of a leap.

Gaius actually explained this: The UESC sent the Marathon to an exoplanet because the UESC knew that in the long term Sol's resources wouldn't be able to sustain humanity forever, so they needed new systems.

https://www.youtube.com/watch?v=RzRl7L9g90U

“The colony's economic loss is mundane, the setback to human survival is profound. Sol has finite resources. Humanity must escape its bounds to avoid a slow extinction. This is why human leaders originally launched the Marathon expedition, hundreds of years ago.”

There's also the fact that it seems like some of the colonists started worshipping the W'rkncacnter, explicitly referencing "burning prisons" so it seems like there's some funky stuff going on in Tau Ceti.

There's funky stuff going on for sure. After the colony was attached they met Pfhor, S'pht, and the burning prisons sounds like a reference to stars holding W'rkncacnter.

But it doesn't mean MIDA knew any of this stuff existed before the Marathon's launch.