"Feeling resigned to just not understanding this one as a lay person."
The biggest and most important step is to make sure you drop any mysticism about what a "dimension" is. It's just a necessary component of identifying the location of something in some way. More than three "dimensions" is not just common but super common, to the point of mundanity. The location and orientation of a rigid object, a completely boring quantity, is six dimensional: three for space, three for the rotation. Add velocity in and it becomes 12 dimensional; the six previous and three each now for linear and rotational velocity. To understand "dimensions" you must purge ALL science fiction understanding and understand them not as exotic, but painfully mundane and boring. (They may measure something interesting, but that "interestingness" should be accounted to the thing being measured, not the "dimension". "Dimensions" are as boring as "inches" or "gallons".)
Next up, there is a very easy metaphor for us in the computing realm for the latest in QM and especially materials science. In our world, there is a certain way in which a "virtual machine" and a "machine" are hard to tell apart. A lot of things in the latest QM and materials science is building little virtual things that combine the existing simple QM primitives to build new systems. The simplest example of this sort of thing is a "hole". Holes do not "exist". They are where an electron is missing. But you can treat them as a virtual thing, and it can be difficult to tell whether or not that virtual thing is "real" or not, because it acts exactly like the "virtual" thing would if it were "real".
In this case, this system may mathematically behave like there is a second time dimension, and that's interesting, but it "just" "simulating" it. It creates a larger system out of smaller parts that happens to match that behavior, but it doesn't mean there's "really" a second time dimension.
The weird and whacky things you hear coming out of QM and materials science are composite things being assembled out of normal mundane components in ways that allow them to "simulate" being some other interesting system, except when you're "simulating" at this low, basic level it essentially is just the thing being "simulated". But there's not necessarily anything new going on; it's still electrons and protons and neutrons and such, just arranged in interesting ways, just as, in the end, Quake or Tetris is "just" an interesting arrangement of NAND gates. There's no upper limit to how "interestingly" things can be arranged, but there's less "new" than meets the eye.
Unfortunately, trying to understand this through science articles, which are still as addicted as ever to "woo woo" with the word dimensions and leaning in to the weirdness of QM and basically deliberately trying to instill mysticism at the incorrect level of the problem. (Personally, I still feel a lot of wonder about the world and enjoy learning more... but woo woo about what a "dimension" is is not the place for that.)
The biggest and most important step is to make sure you drop any mysticism about what a "dimension" is. It's just a necessary component of identifying the location of something in some way. More than three "dimensions" is not just common but super common, to the point of mundanity. The location and orientation of a rigid object, a completely boring quantity, is six dimensional: three for space, three for the rotation. Add velocity in and it becomes 12 dimensional; the six previous and three each now for linear and rotational velocity. To understand "dimensions" you must purge ALL science fiction understanding and understand them not as exotic, but painfully mundane and boring. (They may measure something interesting, but that "interestingness" should be accounted to the thing being measured, not the "dimension". "Dimensions" are as boring as "inches" or "gallons".)
Next up, there is a very easy metaphor for us in the computing realm for the latest in QM and especially materials science. In our world, there is a certain way in which a "virtual machine" and a "machine" are hard to tell apart. A lot of things in the latest QM and materials science is building little virtual things that combine the existing simple QM primitives to build new systems. The simplest example of this sort of thing is a "hole". Holes do not "exist". They are where an electron is missing. But you can treat them as a virtual thing, and it can be difficult to tell whether or not that virtual thing is "real" or not, because it acts exactly like the "virtual" thing would if it were "real".
In this case, this system may mathematically behave like there is a second time dimension, and that's interesting, but it "just" "simulating" it. It creates a larger system out of smaller parts that happens to match that behavior, but it doesn't mean there's "really" a second time dimension.
The weird and whacky things you hear coming out of QM and materials science are composite things being assembled out of normal mundane components in ways that allow them to "simulate" being some other interesting system, except when you're "simulating" at this low, basic level it essentially is just the thing being "simulated". But there's not necessarily anything new going on; it's still electrons and protons and neutrons and such, just arranged in interesting ways, just as, in the end, Quake or Tetris is "just" an interesting arrangement of NAND gates. There's no upper limit to how "interestingly" things can be arranged, but there's less "new" than meets the eye.
Unfortunately, trying to understand this through science articles, which are still as addicted as ever to "woo woo" with the word dimensions and leaning in to the weirdness of QM and basically deliberately trying to instill mysticism at the incorrect level of the problem. (Personally, I still feel a lot of wonder about the world and enjoy learning more... but woo woo about what a "dimension" is is not the place for that.)