OK but seriously, I don't think there's a working definition of 'hard science fiction' that includes Mass Effect.
Sorry, I saw this in the Gundam tag this morning and it's stuck with me and also connected in my brain with the reaction I had recently to somebody calling Alien hard sci-fi, which, well, no. Not really.
Hard sci-fi is a smug, exclusionary term designed to privilege stories based on extrapolation from currently understood scientific laws. It's also a fuzzy category without cleanly defined borders. There are absolutely stories that meld 'hard' elements with more fantastical ones. However, at its core, the concept is describing a concern the author has for being scientifically accurate and how their narrative extends from this. The example I immediately think of is The Cold Equations, which exists as an exercise in describing how to kill teenage girls with physics. The point is to showcase the consequences of mass-to-thrust ratios (in the most mean-spirited, idiotically-engineered way possible, but still).
Mass Effect fails to fall under this umbrella not just because it features things like FTL travel via artificial gravity, magic powers brought on by exposure to same, and telepathy, but also because, as a story, it's not terribly concerned with problems stemming from science. If we were generous, we might say it's exploring the sociological implications of artificial intelligence. Except its grasp of those problems is rooted in a pop-culture understanding of metaphors for slavery, workers rights and racism, not the science of replicating intelligence by artificial means. Plus of course it's ultimately a heroic narrative about unifying disparate factions to face down an unspeakably ancient evil force bent on destroying the galaxy and hang on a minute this is just the B-plot of Lord of the Rings again.
In the same way Alien owes a far greater debt to Lovecraft than the big names in hard sci-fi, Mass Effect is in the vein of space opera and fantasy action-adventure stories. How they look is incidental: hard science fiction is a writing approach, not an aesthetic.
But you know what is an aesthetic? The 'realism' you conflate with hard sci-fi throughout your post.
The easiest way I can think to summarise the realist aesthetic in speculative fiction is visual continuity with the world as it exists at the time of writing. It's useful the first Iron Man film is a good go-to example of this, because it's something frequently found in pop-culture works positioning themselves as contemporary to their audience. Technology is bounded by the appearance of modern devices, fashions and buildings resemble existing examples, and any fantastical elements are textured so they don't seem out of place in such environments.
There are a lot of manifestations of this approach. Returning to Alien, the environments are constructed so as to create a strong sense of verisimilitude. The Nostromo is tactile, solid, worked-in. We are encouraged to relate to it is as a real place, in much the same manner Star Wars pioneered the 'used future' aesthetic, but without the underlying exoticism. Star Wars tries to make fantasy spaces feel real; Alien depicts a mundane place far into the future. Ultimately both were concerned with appearances rather than being strictly true to scientific understanding.
This accounts for the 'realistic' aspects of Mass Effect too. It's a texture, not content. BioWare wasn't trying to educate the player in physics, they were trying to contrive a reasonable-sounding explanation for how the Normandy could cross a solar-system at sub-light velocities without being detected by every telescope and satellite in the area and thus intercepted. That very act of contrivance owes more to realist aesthetics than to hard science fiction because it's the wrong way round for a sub-genre that prizes extrapolating from scientific concepts. We're not proceeding with the logical consequences of physical laws; we're making excuses for the action unfolding in a certain way.
From what I've seen, that's rather common in military sci-fi.
To return to how I came across your post in the first place, Gundam's Minovsky particles are exactly this kind of dodge. A way to contrive a fog of war and justify the kind of combat the creators wanted to depict. The authors started with the story they wanted to tell and cooked up plausible-enough reasons why things work that way.
'Plausible-enough' is the adjective I believe most readily applies to the realist elements found in these works. They're not meant to be realistic but to have the feel of it. To look solid and sensible even when they are nothing of the kind. In this regard, they're almost giving excuses to the audience. 'Aren't you smart for liking the proper Grown-Up action fantasy that is Gritty and Realistic, not like those Silly Stories with their Magic and their Ray Guns.' Smug superiority again, only even less justified.
For what it's worth, I don't think either approach is dumb in and of itself. The problems start with the assumption they're better than the alternatives, and, yes, with conflating the two. No, hypothetical audience member, you are not a more intelligent person because you like things dressed up as 'realistic', especially when they aren't actually telling realistic stories. Power fantasies are just that, no matter their wardrobe. So are horror stories or stories centred on military tactics.
Anyone can come up with a decent hand-wave for why certain aspects of a story work the way they do. Hard sci-fi is supposed to be about avoiding hand-waving as much as reasonably possible.
(To prove the first half of the last paragraph, the reason you can't use a tactical cloak on something like a ship or shuttle is 1) they're too big and/or are regularly subject to extreme conditions that would rapidly degrade the external components of optical camouflage, and 2) you cannot invisible your way out of sonic booms, engine noise, or the heat and light produced by air friction on re-entry, meaning the tech is basically useless for hiding an approaching spacecraft anyway. All very plausible sounding, no? And functionally distinct from the long range, stealth-in-space problem Mass Effect was hand-waving so we didn't wonder why we weren't dodging enemy fleets until the third game, where the enemy was Sufficiently Advanced a mini-game felt justified.)
(Sorry, again, but I do think you are overlooking that the tactical cloak is a gameplay-relevant feat applied to human-scale characters to spice up the combat while the stealth frigate stuff is specifically downplaying questions about how a starship can casually fly into observable range of planets crawling with hostile, technologically-advanced beings without being immediately shot down by every missile the Geth have at their disposal. Sometimes games, specifically, are like that, because they can't afford to make everything consistent and fun or even cool.)
