I feel like rules supplements can be hard to write and harder to find a niche because people run OSR games in such wildly different ways, especially Mothership. For my style of play at least I feel like I'd have difficulties using this without reworking further. There's definitely a solid foundation here, especially tone-wise, but after a quick playtest I find the mechanics themselves a bit confusing and question if my players would have a terrible amount of fun repeating this after the first attempt. That's not to say there isn't stuff I like, a lot of this scoring is more related to what I get out of supplements like these more than anything.
But still, please keep working on content like this! Rules-focused supplements are few compared to the adventures out there, and I really like yoinking different ideas from modules like these to flesh out the systems of games I run. There's something good here with the node-based nexus whack-a-mole you got going on for sure.
Polish - 3/5
I really liked the writing style you went for, feels as if it's written by a hacker trying to give you a low-down on the trade almost. I feel like it could have leaned further towards that direction but it also gets hard because you have to attempt to succinctly and clearly describe the procedures you're trying to introduce. I think you did a good job at separating the two tones for the most part. My only critique is that the explanation of many of the mechanics tends to be a bit confusing to follow, particularly when the layer jumping is involved and skill checks are starting to frequently be made. Trying to simplify the steps and formatting them better could go a long way. A better visual flow indicating the order you go through when hacking would be helpful, something similar to a flowchart design between rules sections maybe?
Layout-wise it gets the job done. I'm not a huge fan of the colors being used and the way the blue text you used is highlighted and italicized can be a bit hard to read. The in-world advertisement feel you had for the hacking gear would be a really cool aesthetic to lean further towards honestly. Also gotta say, really like the cover art. It's cute and fits well with the theme and tone of the supplement.
Favorability - 2.5/5
The low rating is honestly because I just have a hard time visualizing what I'd get from this mini-game versus using hacking checks as-is and describing what happens a bit more narratively. In my experience separate "games within a game" systems like this can be super hit-or-miss because they need to warrant the time you stop playing the main in order to play through it. Hacking is a classic mechanic that typically gets this treatment and many takes have the same issue: unless multiple people present are playing hackers, it turns into everyone else waiting for the hacker/Warden to make a dozen rolls to see if they get what they want or not. Especially if it's something that the entire session hinges on: the access code to the vault they're trying to break into, stopping the AI relentlessly hunting them down, clearing their name of any crimes logged in corpo records. So the mini-game should ideally be A.) quick to run through and get game-able results from or B.) generate results that are interesting enough to justify the mechanics you're engaging with.
My favorite part still has to be the informal hacker tone that influences a lot of the writing. Makes it an enjoyable read even if I don't mesh entirely with the mechanics present.
Usability - 2.5/5
As written this involves a lot of rolling at certain points. The mechanics for it themselves are relatively straightforward, it's just the way they're explained and written requires some cross-referencing between sections and minor creative interpretation on the Warden's part to make work. I did a short solo playtest running it and it felt like it involved too much rolling that didn't necessarily result in interesting results. Succeeding largely just lets you avoid stress and move around a bit further. Failure isn't great, but you're still making progress and only ticking up 1 per failure. Just kind of felt like I meandered around a node until I got what I wanted, then it just boiled down to hoping I'd beat the matching d10 rolls I accumulated during the dive. The items are essentially the only way to get further agency over the game, but they're incredibly powerful and priced in such a way that I see most players grabbing just logic bridges and division swarms if they want to get through the hack efficiently.
Don't get me wrong, I like how you incorporate a narrative element the player directly benefits from which is baked into the procedure itself. Leaving the rewards and consequences up for the Warden to decide and talk about with the players is the best move as opposed to trying to establish a catch-all procedure for what they get out of the task. It just feels like there's a lot of rolling happening while nothing is really happening round-by-round except a "hotter/colder" type mini-game. The active threats you describe could definitely spice things up a bit, but I feel like the process might be a bit more annoying in play than it is rewarding.
Theme - 2.5/5
Beneath the surface being interpreted as the inner workers of an AI's defense against hacking is interesting, but the theming loses that focus as the rules turn more into generalized hacking procedures. I think narrowing the focus for it being a specifically AI-related mechanic could give it some more focus and let you write in flavor regarding them in your style of writing that'd be fun to read.