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I’m a year into my guitar journey and I still have trouble always picking the correct string. So first off, go easy on yourself and realize it’s going to take time.
Whenever you are struggling with something on the guitar the steps to do are to simplify, isolate, and slow it down. Your brain can’t learn two things at once, so if you are fretting and picking, the brain is going to learn whichever you are focusing on the the most and if you are bouncing back and forth between the two it will probably learn neither very fast.
For picking don’t worry about your fretting hand and just practice the picking. Whatever that pattern may be. Start slow and speed up over time. Use a metronome. The rule of thumb is that if you can play an exercise 3 times in a row perfectly then speed up. If you make mistakes 3 times in a row slow down. You need to practice a skill consistently (at least 3 times a week), to really commit it to your subconscious.
Another tip for flatpicking is to put your little finger on the pickguard. This gives your hand a reference point. Over time your brain will learn how much to move your pick to hit each string.
I spend 5+ mins everyday doing dedicated picking practice with a metronome. Some patterns I can learn in a week. The one I’m currently trying to learn I’ve been working on for 4 weeks. Started at 50bpm and now up to 85bpm (the goal is 100bpm for this song). It’s a process but it works.