Is this a door going to the inside of your house or outside? Can you just change the swing so that it swings out of the garage instead of in?

Does this affect how the hinge pin door stops would work?

Those are a poor choice for this application. They are intended for light weight interior doors.

" Does anyone recognize the type of hinge I posted in the picture above? It looks different than standard hinges on all my other doors. "

Those are self closing hinges, they will not effectively work to stop a door from opening to far.

105S-716 Glynn Johnson 100 Series Heavy Duty Concealed Overhead Stop. Or similar

Can you swap the shower and the other bathroom and move the door closer to the tub? That would give you a place to hang towels closer to the shower and prevent someone from walking straight into the side of the vanity.

The neighbor's design is a typical suburban infill lot concept, just a little stretched.

The seller's design seems to be designed for the site (it was designed by an architect for someone and someone's site somewhere). If you notice, it has a very strong view axis towards the Northwest. A lot of the plan's concept revolves around views and having access to them throughout the house. The opportunity for value level seems appropriate for the high end of this region.

So if this seller's design indicates assumptions about your site, your proposed plan does not meet those well. But, with the symmetrical concept and framed view, where I wouldn't blink an eye is if I saw it on an urban infill lot on the intracoastal in Florida.

Jumping in on the steam shower spec, since that's a different animal than a regular shower build: the ceiling needs to be sloped (not flat) so condensation runs down the walls instead of dripping on you, and the whole enclosure — walls and ceiling — needs a continuous vapor barrier behind the waterproofing, not just the standard shower membrane. You'll also want a fully sealed steam door (floor-to-ceiling glass with a tight bottom seal, not a standard shower door with gaps at the bottom) or the steam just leaks out and the generator runs constantly trying to keep up. And make sure whoever sizes your steam generator is calculating off the actual cubic footage of a 4'x6' enclosure with your ceiling height — undersized units never get hot enough, oversized ones short-cycle and wear out early. Worth confirming your contractor has built a few of these specifically, not just standard showers.