Turntables, phono stages, valve amps, are the sorts of things that would be susceptible to vibration. Solid state (aside from maybe MC stage), shouldn’t be affected by vibration. IMO hifi furniture, dampening/isolation, etc. is just foo for solid state. RoA is on the right track that your new cabinet could have modified the room acoustically.
BTW here’s a nice article about an experiment that went to some extremes to show that microphony is not a thing for solid state:
https://www.audio-forums.com/articles/microphonic-effects-on-solid-state-circuits.17/
Whenever this link has been posted in threads in the past it usually gets ignored.
Are we actually mostly agreeing that an afternoon of inexpensive trial-and-error is the next step, whatever the underlying cause of he problem is?
It's always easy for those of us who are more subjectivist rather than objectivist (if you see what I mean) to find reasons to ignore test results - e.g that link. Good, but perhaps over-used examples might be: -
1. We don't have a proper model for how the source data gets to our heads that enable us to tell how people will report the SQ, and until we do we can believe in supports, cables or turntables if we want.
2. We don't actually know all the things that need measuring, but we do know that an unvarying pink noise input may not be representative of music (or spoken voice).
3. Formal models for rooms (see concert halls) are fiendishly complicated and long-winded, and still need checking with ears. A smaller listening room is all the more likely to have individual features that have a major effect on SQ, so producing any answer that can be generalised usefully is harder than it looks.
Other people can just as easily point to snake-oil salesmen and their lack of veracity and how rare a proper blind test of anything is, and how variable our perceptions are and how poor auditory memories usually are, and a host of reasons why caution is needed. Some go to extremes and assume that the graphs are right and all we need to know, and that what we think we hear has nothing to do with getting a more enjoyable hi-fi (see perhaps ASR). Pretty soon, the thread has descended to some people suggesting that anyone with different results to them must be deluded/ deceived/ dishonest or deaf.
None of that really helped me when I tried investigating isolation, and it probably won't help this OP either - party because it's apparently an unending topic and partly because these things are (in my limited experience at least) all about the specifics.
As people here have said, it is hard to form a view on whether the cabinet is absorbing and radiating a significant amount of sound, or whether the boxes vibrate on the shelves in a way that is audible. We can't tell whether to be concerned about transfer through the air or via the floor or both, and noises of these sorts need not be at all obvious to have an effect on SQ. My guess (like yours perhaps) would be that the cabinet is an accidental passive radiator and sounds like the world's worst sub-woofer, something that the OP can probably test by taking the door off or (less good) hanging a jumper on it.
While it would be weird to put microphony in a solid state amp high on a list of suspects in any room/ system, I'd argue that we know that we don't know enough (and 'we' here can be pretty wide) to diagnose what is going on, so thinking about the mechanism won't help.
Fortunately, there are things the OP can try without spending money or doing anything irreversible - as several old lags here have said. I tried various woods, granite, glass, MDF and more - with standard hi-fi box feet, rubbery feet from HRS, balls-and-cups from a Fraim and various bits of sorbothane. I used multiple listeners with notepads and stood as consistently as I could in front of the rack. Some options were obviously awful, but the rest were clearly not identical if you listened hard enough. How the supports (and any object in the room) affects sound may be hard to predict or model, but it is surely easy to detect with ears if it is a real problem (as here). We were born with the tools....