unrelated Col Lore (TM) that i forgot about it until just now. The Col is actually a conglomerate of like, 5 or 6 of the Empire's "best and brightest" who were unwillingly cannibalized into one machine. He was created at the behest of the tiny circle of lords/councellors/commanders who know that the god-king is dead, originally so that he could be a facsimile of the god-king that they could parade around to quell doubt about his absence. He's also a nexus of administrative knowledge and "forbidden" history, and probably served a more tacit purpose as an arbitrator between the vying Powers That Be.
That's not saying very much about his power or agency in all of this. Still a puppet of power with many restraints put on him, given the sensitivity of his creation/operation, which has taken Many Years. In fact, the whole Markus debacle ended up interrupting this process, so I don't know that the fiction ever got off the ground publicly.
... as for how the Col ended up getting to Earth. well . they were like "we made this supercomputer and we can't even use it smh" so the Legate plugged him into his ark-ship for navigational/administrative purposes when he paid Earth a visit. and then ummmmm 😳 so there's this act of heresy that resulted in the Legate's death, the annihilation of the ark-ship, the escape of the Endeme from Earth, and the irreparable destabilization of the Empire,
now the Col's just hanging out in a tree with the rest of the endlings and airing out the Empire's dirty laundry.