I'll take your word for it, because it sounds wild and unnecessary, you know unless like Rip said, you're building on garbage soil. Still, we put garage slabs on coastal sand where you otherwise have to drive piles to support the house. My big issue with this is why the garage slab is intended to be continuous with the building in the first place. The way we usually do them, even with concrete structures, which are done, is the garage slab is just a simple slab-on-grade, which are always non-structural. Meaning while you definitely put loads on top of them, they're not carrying building loads. You pour the perimeter garage foundation, place or cast your stem wall above it, and then just float the slab inside its perimeter.
I would love to see the slab section and the details for the transition between the floor slab and the garage slab. If I'm understanding your correctly, the designer/builder is continuing the tendons effectively around a corner, really two corners, and hoping to provide enough tension to do what's intended.
Post-tensioning is still generally specialized work. The design of the system needs not more than a fair amount of experience; I did two semesters on it in graduate school, plus some additional work on the detailing of the anchorage design in other classes, i.e., strut and tie models. Seems to be overkill, honestly. I don't think I'd trust tract home builders to go anywhere near it.
Whether you have post-tensioned concrete or not (a term I never knew until this thread), many garages have plumbing underneath. Protecting the floor and protecting the plumbing are two sides of the same coin. Nobody wants to have to repair a supply or sewer line underneath their garage floor.
Are you trying to secure a full rack or a half-rack? We've had many discussions in the gyms/equipment forums about this. Many manufacturers make platforms that (they claim) don't need to be secured to the floor. The rack moving a bit isn't really a concern. Decent racks don't just spontaneously fall over. However, if one leg moves more than the other, they can get out of square to a point where the rack isn't really safe anymore.
I have relatively lightweight rack (Fringe Sport Garage Series) that I bought used during the pandemic when things were slim pickings. It sits on a platform and has weight storage posts where I've put about 300lbs. It hasn't moved any measurable amount in the past two years. Securing the rack isn't to prevent it from *moving* it's to keep it square. Even attaching one to a wooden platform is enough.