Very good job my friend! I was watching a few times carefully to spot some issues but aside of just a little timming problems and maybe one or two moments of unwanted string ringing under, I haven't found anything truly wrong
You have additional points of keeping 3rd part strted with and upstroke (that happens to be forgotten in many takes). I like You clean playing. You picking looks accurate. Muting is clean and tight and there is a good proportion between palm muted and not muted notes. As for the timming at some points it sounds like You move whole phrases in time for just a miliseconds before or after the beat. Maybe it worth trying to increase backing track volume when recording. What's most important - Your picking is consistent and there are no uneven breakes between notes. At 0:31 we can hear that mentioned noise from unwanted strings - yopu need to flatten your left index finger just liek with barre chords (but do not pressure) to get rid of it.
If You want to get even more profit from this lesson I advice to try different type od distortion. You has to have a lot of sharpness due to ability to sound that "crunchy" on neck pickup (especially humbucker" and with a medium picking strength.
Things will get harder if You use different (more muddy, less gainy kind of distortion). It will make you have to play much harder to get wanted amount of sharpness (even on the bridge pickup position) and this will affect relaxed picking hand state you have at the moment. It's not a must - it's an offer for a challenge with yourself
Overall - great job!