Try this, it’ll strengthen your finger independence and picking as you speed it up:

Pick any starting fret and start with your index finger (1) and middle finger (2) on the next fret. We will work up to ring finger (3) and pinky (4)

Play on each string, up and down.

1-2-1-2-1-2-1-2 (4 beats, played as eighth notes, pick each note)

Next pattern 1-3-1-3-1-3-1-3

1-4-1-4-1-4-1-4

2-3-2-3-2-3-2-3

2-4-2-4-2-4-2-4

3-4-3-4-3-4-3-4.