These are great questions to ask about Archives, and the answers your table comes up with should give you a lot of fun technical ideas for how to use the Archives and timeline to flesh out the mechanics of how World works. I really think you are both on the right track, so I won't speak much to the setting stuff: you've already got this.
But since you brought up the nature of the Restore function and the examples in the Function section, I figure that I would say some things about the philosophy of assigning Complications as a GM. Restore, just like any other function that the players try to do when there are interesting or dangerous obstacles in their path, is fallible in various ways. So it might just be that while there are versions of the Safe that have what the user wanted in it (i.e. the 6 result on the die roll that the player missed in their dice roll), for some reason in the moment they weren't able to line things up. As GM when you get a result of a 5 or less, you have a lot of freedom to narrate how things go less than perfectly. One way to describe Complications is to emphasize the challenge of taking action under all the pressure that the users are in during a score... things like Time (are guards about to stumble on us as we fumble with the safe? Does that make it harder to do things perfectly?) or Deniability (can I mess with the safe in a way that doesn't make it obvious what I did? Does my user make an error through an overabundance of caution?).
When I GM for a Forged in the Dark game, during Scores I find an effective approach to my Complications is to emphasize the powers and capabilities of the opposition (in preference over narrating the players bungling things or failing on their own terms). This way the players are assured that while their users are powerful and capable, the factions they are going after are just as strong and just as cautious as them. I did my best to showcase this style of consequence in the function sample scenarios, which is why you might be seeing complications that seem a bit complicated. "Why not just tell the players that it didn't work because they did badly?" is a non-starter a lot of the time both because it can be demoralizing for some players, but just as importantly because it often doesn't advance the action in a dynamic way!
Don't forget also the most important part of a Forged in the Dark game: the ability of the players to Resist any consequence they don't like! The player in the example scenario might next say "You know what, I think that my user won't take no for an answer. I'll make every effort to beat their security because I really want to get what's inside the safe! I can just resist that Reduced Effect consequence and push on through the distractions... we see beads of sweat form on my user's brow as his focus narrows to a pinprick." Then they would roll some dice (based on the surrounding fiction, this could be either a Stability, Resolution, or a Computation resistance!) and maybe take a little bit of stress, but they get what they want!
