Hello, driving enthusiast here.
Driving was stressful for me to learn as well. But i picked it up pretty quick. I learned in an auto and learned manual later which took some practice.

This all being said, like anything else, you are only finding manuals distracting because you're still learning and they aren't second nature. once you don't have to think about driving a manual it won't be distracting. automatics are the distraction problem, imo, because they allow drivers to play on their phone instead of driving.

I've only ever fallen asleep while driving an automatic (twice), never a manual.

You are frustrated while you are learning and that's to be expected but don't you dare go blaming your problems on others, such as cyclists. Being a poor, distracted, and terrible driver is your fault and your problem. If you can't handle driving around other people then stop driving.