| Hithesius |
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Alright, let's break this down then. You want to recreate the Astro Megaship in Starfinder. I can tell you immediately that for the time being, turning into a mecha and cutting enemy ships apart with a giant mech sword is something the rules won't support. I know someone's working on a ruleset for mecha - though that may be third party - but for the time being, that particular part is out. Unless you want to homebrew something yourself, of course.
Unfortunately, that wiki page on the Megaship itself is somewhat light on some relevant details. Fortunately, the original Sentai version has somewhat clearer numbers. A length of 37 meters puts it on the bottom end of the range for a Medium ship. Personally, I'd go for the Transport frame - it's slightly more expensive, but it has an extra expansion bay.
The weapons are slightly trickier because of how SF handles arcs, but it can still be approximated. The double-barreled cannons could be mounted on the turret to give them the 360 degree field of fire, though they couldn't shoot in different arcs at the same time. Maybe upgrade both turret mounts to heavy, and fluff heavy laser or plasma cannons as being double-barrelled. I can't speak for the ion cannons, because different people and settings use names like that in different ways and I don't know what it's supposed to be here.
The wiki article says it can be run by as little as 1 person or even auto-piloted, but houses up to 16. Transports can handle the low end, and you can either spend two expansion bays for guest quarters (total capacity of 18), or maybe just spend one (capacity of 12) and handwave the remaining four seats. You're the hypothetical DM, you can do that if you want. By the rules that's still only 6 active combat roles, but you can probably work with that. Or work around it, if you really need to.
Explicit FTL travel means you have a drift engine. A training room is probably best modeled with the top level recreation center, fluffed as whatever the training room actually involves in the series. Just skimming over the wiki articles, I don't see anything that says other expansion bay would be needed.
Without any more details of what exactly you're looking for, I can't really give you more than that kind of general thoughts, though. You'd want shields, sensors, thrusters, and a computer of some sort, and obviously a power core for all of this as well, but I don't know what kind of tier or anything you're aiming at here.
If you can give more specifics, I could throw together some example builds. Or you could even fiddle around yourself! Personally, I've used this spreadsheet, but if you look around you might find some others on the board to help with this.