So if I'm interpreting this right, you're struggling with less space between notes and having to hit them faster. And to be honest, who doesn't ever? Are you able to hit these notes in this order at this manageable speed? Neat. Are you able to do it but noticeably faster? What's that, you're struggling now? That's pretty normal.
That said, I can't ignore that (at least from what I know of 3* not having played 2*) is that it is when a lot of new patterns and ways of hitting notes are introduced (and if I'm wrong about that, lmk). It really comes down to learning those new ways of hitting notes... slower. Like for example, when I was practicing splittrill JS and HS a long time ago, I determined which ones were too fast for me and set them as a series of goals, and got really good at them. I had to start slower though.
And ofc, there's the paradox of "if 3* is doing these more advanced patterns at simultaneously a faster speed, how do I find practice for it?" which is why half-time and decreasing speed on songs is incredibly helpful (or at least was for me progressing 4*).
(THERE IS A TL:DR BELOW THIS, AS I REALIZED I AM A PROFESSIONAL YAPPER)
uncollapse this if you find it too long
As for how to read notes, there is a lot of things which goes into it. Just think of the notes as rows of scrolling inputs while reading this, as it's easiest for me to explain like that.
Firstly, scroll speed matters. What people do to decide their scroll speed is figure out just how many rows they want to see at a time at a certain speed and depending on the patterns they are playing. For example, my scroll speed is 24 because I want to read more notes at a time, them and preact to them. Most people use faster, resulting in more reaction-based gameplay. And more importantly, this can change overtime. I used to use 22 a long time ago before it stopped suiting my needs in reading notes.
Secondly (AND THIS IS WHY THE TL:DR EXISTS) is chord recognition, which then plays into pattern recognition. Each row scrolling (aka each note) requires a different input, whether that be on a single lane or two or more. But you eventually have to start associating these rows of inputs together in a grander picture. "If I see the notes go 1 2 3 4 23 1 2 3 4, I tap my fingers 1 2 3 4, 23, 1 2 3 4". Maybe you read the 23 as 32 to follow the direction which the notes zigzagged, that's another way of reading it (tho eventually most will generalize this). As well, you may read something like "3 3 2 2 14" as "two taps at lane 3, then two at 2, then an edge-double" (again, will eventually be natural enough to generalize). And then there's more subjective ways of reading notes like " 4 14 4 24 4" as either "do a single then double" or "just keep tapping 4 and press the other ones when they approach" (do I need to write it again?).
And then the spacing is the hardest part. You will need to read how much space is between notes, both to figure out how fast you will need to tap and to also figure out how many rows you want to merge and read at once.
And that will eventually develop recognition for the pattern you struggle at.
TL:DR
Reading patterns usually requires reading rows of notes/inputs together rather than individually, which you judge via the spacing between notes. Being able to recognize and hit chords will make pattern recognition easier. Adjusting note speed to be flexible to how much notes you want to read at once at a certain speed for certain patterns matters and is subject to change over the time you play.
It's probably more complex than that. I just wanted to keep it in the realm of normal notes since my LN is pretty weak at the moment, though most things I said will still apply to LN albeit with more nuance. Anyone is free to challenge me on what I said.