How does an Imperial prison work?
I would imagine that there is no such thing as a single "set" way that Imperial Prisons work. Due to the hands-off attitude of the 3I, local authorities seem to deal with crimes as they see fit. Correspondingly, most "high law" crimes in the 3I probably carry death sentences, which conveniently eliminates the need for prisons.
How would one organize a prison break with the Orwellian technology available to the 3I?
An interesting way to look at such things is to consider that the 3I is inherently a
human Empire, that is, it is run by people instead of AIs, or aliens who are idealized parts of the human psyche. Because it's run by people, you can expect human failings to enter into it, even at TL15:
First, let's say a planet has a prevailing view that criminals can't really be "cured" - once a criminal, always a criminal. This is actually the kind of world you probably want your players to come from as they have a suitable "lock 'em up and throw away the key" attitude. Such a world wouldn't really want to invest much in rehabilitation. Perhaps they don't want to kill criminals outright because of the outcry of human rights groups in Capitol. However, since they consider criminals essentially "flesh failures" they probably wouldn't want to spend much money on them. Taking a cynical page from our own world, perhaps such a world doesn't want to deal with criminals, so "outsources" them - dealing with prison populations by sending them to another world and...
* Perhaps the world is lower-tech, taking criminals from higher-tech worlds in exchange for technological assistance/goods from higher-tech worlds. Treaties would exist to process the criminals to make sure they have no implanted high-tech devices. Given the high tech existences these prisoners had, escape would be difficult simply by the fact these people have no idea how to survive in the wild, datahackers wouldn't have any computers, and gruelling and most cruel punishment would simply be things like having to go to bed when it gets dark if the primary lightsource at night are expensive candles and having no vid to watch. The world itself might be very low TL (like just described) or somewhat higher TL, giving you the option of making prisons patterned after any number of historical Earth examples. Perhaps the world is a natural prison planet - some unusual conditions in the system's sun and the planet make for amazingly savage radiation belts around the world, like the same as a meson gun going all all the time. Only specially shielded ships can get to and from the planet, and only from a tiny starport on the other side of the world. So the players would need to cross this savage, medieval world, then get on creaky ships like from 1492 and sail across the great seas to get to the starport, then find some way to bribe/sneak aboard the shielded ships to leave the world...
* Alternatively, perhaps the world itself has some very different social structure. Like some months ago, I brought up a world in a thread about slavery on this board that uses neurochemical processes to eliminate the writing to and access to most of their of long-term memories. Such prisoners could be put to work doing the most menial and repetitive tasks and never get bored of them (entertainment is easy, find an album they like and set it on repeat - by the time the album is over they forgot they heard the first songs...). Perhaps there is some natural disaster or some similar infrastructure failure and the players remember who they are. Some people perhaps regret the terrible things they did and actually requested being sent to this world so they could forget their past, while others might be natives of the world and use the society's methods to keep from getting bored of their jobs and yearn for control to return. Of course, the players wouldn't want to be and would have to find some way to hide or escape.
On a totally different view, perhaps the players are shipped to a world that is strongly matriarchal and has a strong respect for tradition, social ritual, gender roles, and order. They're kept in a prison away from the rest of society. Escape isn't impossible, however, since the prisoners are deliberately prevented from socializing outside of the prison, prisoners stick out. If your players are playing male characters, this is easy - an assertive man on such a world would stick out like a sore thumb. Even with female players/characters they would still stick out because they don't know the proper customs or would treat men as their equals. The trick of such a place would be to somehow blend in well enough to make it to the starport, again...
* Perhaps the world has no qualms about use of neurochemical processes to "correct" deviant individuals. Akin to Larry Niven's "The State" - perhaps the world routinely processes criminals by mindwiping them and recording the personalities loyal and valuable citizens who recently died. So the players are released onto the world and tattoo'd or something. Provided they never screw up again, they'll be fine. If they do, they "die" but since the execution isn't physical, human rights groups are a little more forgiving of it. Perhaps due to the expertise of the world in such things, "capital crimes" players are sent here to be mindscrubbed and have their personalities overwritten. However, since the doctors performing such things are people too, perhaps it is possible to bribe the doctors and have them claim the surgery was done when it really wasn't...
