Not my spouse, but my mom is skilled in the "art" of passive aggression. She is deeply uncomfortable with/avoidant of overt disagreement, but will often make sideways/backhanded/covert/ambiguous comments. I have known her long enough (and am fluent enough in girl-speak) to know exactly what she's saying when she does this, but her 'criticisms' are incredibly difficult to address or respond to because she's not saying things directly, and she will typically backtrack if I call it out ("I didn't say that, that's not what I meant...") When there is an actual argument she's like a fish out of water and will escalate quickly or jump to the "fine" followed by the silent treatment type technique that you are describing in your wife.
It used to drive me absolutely crazy when I was younger, until I read more about it and gained some more understanding of what was going on. Being able to name/identify the behaviour in the moment (versus feeling attacked/frustrated by little barbs I couldn't respond to) was huge for me in seeing it for what it actually was (her way of voicing a criticism). Literally just naming it prevented it from getting under my skin so much. Understanding it and where it likely came from, also allowed me to have some empathy for her - instead of just lamenting over why she couldn't voice her opinion and "have a discussion like a grown up". (Quote from an actual conversation I had with her once)
I have no idea about your wife, but here is what I have worked out about my mom (in case you see any similarities). She grew up as the youngest child in a pretty chaotic household (father was an alcoholic). There was a lot of tension in the house and I suspect some violence. One of her older siblings was a bit of a 'wild child' and caused a lot of additional disruption, and my mom spent a lot of energy trying to keep the peace amongst everyone by not rocking the boat. Her father was not to be challenged - certainly not by a (female) child - and she eventually learned not to speak up. Because conflict often resulted in hostility, any perceived disagreement became a trigger and set her nervous system on edge and was to be avoided. She also grew up in a larger societal culture where women (and especially girls) were not rewarded for speaking up and having opinions. Quite the opposite - "good girls" were submissive, quiet, passive and kept their heads down. "Loud women" on the other hand, were criticized, chastised, and judged. So my mom, like a lot of women, I think, learned to communicate in more subtle, "socially acceptable" ways.
Fortunately (for me!) my mom didn't completely internalize all of those beliefs, and went on to raise an often-headstrong, super-direct, ENTP/ENTJ type daughter. When I was younger we butted heads because our communications styles were so different. While I know she is proud of who I am and I love her enormously, she's also totally ill-equipped to respond to me as an adult (vs. a child) sometimes. I imagine she is exhausted by me constantly trying to push her out of her comfort zone, and I find myself exhausted having to dance around a bunch of ambiguous comments to encourage her to get to the point.
We had a "blow out" conversation once several years ago during a visit where I calmly pointed out to her how frustrated I was by her passive aggressive comments and was able to provide many receipts/examples when she predictably demurred/backtracked/had "no idea" what I was talking about), and she got emotionally escalated and eventually shut down the conversation, and it obviously didn't feel great in the moment, but I know she respects/loves me and she did go home and spend a bunch of time googling/reading about it when she was less worked up and I think some of it resonated with her. I do my best to stay calm during it and will repeat back to her what I interpret her concern/criticism is in a way that (I hope) makes it feel safe for her to share her opinion. Her first instinct is often to deny/downplay it, but after our conversation she will now sometimes voice the opinion (often in a more watered down way than I received it) and that is progress for us. To be honest, it's so ingrained in her, I truly don't even think she is aware of it, and so the ability for each of us to call it what it is in the moment can be super helpful in avoiding it.
Hippo - it sounds like your wife's particular "brand" of "passive aggressive" is stonewalling. Super difficult to have a productive conversation with someone who does that. Have you read much about it? Gottman writes about it as being one of the Four Horsemen of the Apocalypse in relationship communication. Essentially it's a manifestation of the "freeze" reaction to danger, that someone may feel when they are physiologically flooded. Shutting the conversation down allows them to avoid it. My husband tends towards freeze in his reactions to conflict too (and it took me a while to understand that this was a lot less manipulative/deliberate than I was interpreting). That didn't make it acceptable obviously, but it altered my reaction to it. This was the type of thing that I found marriage counselling actually really useful in addressing. Is this something you've tried?