I believe the Fret Hand (left hand) is the more important half of guitar technique. It’s easier to build speed in the picking hand (right hand)*, even at lower skill levels. So that tends to be focused on more, in this forum especially. Not that picking is not important, but when you play single note lines (that are at least 50% of most solos), the speed limit is dictated by the fretting motion more than the picking motion. This is because hand sync is limited by the speed of fret hand physical skill (a combined control of finger movement, dexterity, strength, speed, and accuracy), and the speed of your mental power (a combination of visualized / audialized patterns, thoughts, feelings, memory, and nervous system).
Of course the intricacies of pick mechanics are covered in extreme detail here, but it’s a simpler movement once you find a motion that works for you. It’s ultimately just finding the optimal way to get the pick up and down on a string, and learning to efficiently change strings. The right hand can much more easily find a rhythmic groove with a smoothly flowing left hand, but having a weak left hand will prevent you from reaching your fastest picking speeds.
Another fact is that in ‘standard’ right handed orientation, the left hand is the ‘off hand’ or weaker hand for most players - this makes control more difficult and requires more training than the stronger hand. Without special training and focus on the fret hand alone, you might end up with just a strong tremolo, or an overly ‘stiff’ feel if you focus too much on picking every note. It will feel much more forced sounding, and IMO it makes playing more difficult than it has to be.
So Legato practice is the other thing that needs to be looked at. This is basically left hand solo (fret hand only). You are allowed to pick the first note of a string, but then you will connect all notes on the same string with only Hammers and Pull-offs or Slides (at least to start getting a grip on the technique).
I like practicing patterns with different notes per string (NPS): 2NPS (Trills, Pentatonics, and 7th Arps) | 3NPS Scales/Modes | 4NPS Expanded Scales/Modes | 1NPS + 2/3NPS Arpeggios.
Play Trills with 2 notes on 1 string - varying time from short to long, varying speed from slow to fast (or vice versa) - also between free time and in rhythm with metronome/drums. This will build speed, accuracy and endurance over time.
Playing trills between every finger pair builds dexterity and stamina: 1-2 | 1-3 | 1-4 | 2-3 | 2-4 | 3-4
This order is the easiest to hardest trill motion (or most to least ergonomic) IMO.
To take this up a level, use wider intervals (with a gradual progression. Ex: 1/2 step (m2) | 1 step (M2) | 1.5 step (m3) | 2 step (M3) | etc… as far as you can comfortably reach between each finger pair. You will not have the same reach between each finger pair - it’s easier to stretch with 1-4 or 1-3 than with 3-4. This can be dangerous if you over-extend in stretching, take this slow and stop if you feel pain.
3-note legato rolls on 1 string (descending pulloffs or ascending hammers) are a good level 1 exercise. Combine 2 strings for a 6 note descending or ascending pattern for level 2. Work up to 3 strings, then 4, 5, 6, etc… There are lots of combinations you can create and discover. Finger combos are: 1-2-3 | 1-2-4 | 1-3-4
You can take this up a level with 4-note per string patterns on 1-2-3-4
or with slide-shifts: 1-1-2-3 | 1-1-2-4 | 1-1-3-4 | 1-2-2-3 | 1-2-2-4 | 1-3-3-4 | 1-2-3-3 | 1-2-4-4 | 1-3-4-4
These are basically all the finger combos you will ever use in 3 + 4 NPS scale/mode patterns.
Eventually you can try string changes with only hammers (no pick) - this is the ultimate legato that Holdsworth, Van Halen, Michael Romeo, Brett Garsed, Marshall Harrison all do very well (among others). Michael Romeo has some incredible left hand tapped Arpeggios in videos that demo the 1NPS legato technique (see Guitar Chapter).
A big thing in the technique of Yngwie, EJ, Van Halen, Vai and many others - is combining legato with picked phrases. They often combine alternate or sweeping motions with pickstroke+pulloff or pickstroke+hammer combination (or multiple pulloffs/hammers/slides). Combining picking and legato gives different articulation, dynamics, and rhythmic feel compared to Legato only or Picking only techniques. There are mechanics that flow very smoothly in a combined left+right hand technique, where everything is highly synced and coordinated, but this takes a lot of skill. This is all covered through CtC material, especially the Volcano and Cascade seminars.
Note: my comment applies equally to left handed players, just flip the left+right hands.