I feel like sleep matters a whole lot more for chess than I realized at first

look at your ages circadian cycle and figure out when its best for you to sleep and wake up. Doing this will heavily improve how much you feel
Sleep is important for the memory and cognitive functions.
About nutrition and execrcise:
https://handbook.fide.com/files/handbook/Nutrition%20and%20Exercise%20Doc.pdf
@8
There are more mistakes than that.
At some time I noticed I often lost concentration and blundered in over the board classical games after 4 hours of play. Yes, blunder, time trouble, fatigue... Then I realised it was low blood sugar level. I made it a habit of drinking a coffee or tea with 2 sugars and the problem was fixed.
Alcohol is of course very bad for chess, even 24 h after intake.
Try to sleep at least 56 hours a week, but it is better to try for 6 more hours of sleep, on a Sunday or Friday with a lot of sleep. If you add at least 4 more hours of sleep a week you will notice the benefit on your mental health. That is, sleep between 60 or 62 hours a week if you want to train your mind, mental activity requires additional hours of sleep to get the most out of it. Combine that with enough physical exercise and a diet without junk food, I won't tell you what you should eat, but do your own research on diet; but do not adopt the vegan diet, it is not recommended for people who train their brain (b12 deficiency can drive you crazy).
Small changes to your diet could bring improvements to your performance, for example stopping consuming sweeteners or consuming much less of them. Try to eat one or two foods that are nutritious for your brain.

Even if I feel fine and I feel perfectly awake, if I am behind on my sleep, something is "off." I just don't see moves properly. I dropped 200 points of ELO from not sleeping and only realized after I finally started sleeping properly that it was due to lack of sleep.
I think its more about being energized, even if you sleep for 10 hours, you won't do well if you feel tired.
Even if I feel fine and I feel perfectly awake, if I am behind on my sleep, something is "off." I just don't see moves properly. I dropped 200 points of ELO from not sleeping and only realized after I finally started sleeping properly that it was due to lack of sleep.