Filters don't really "Clean" that tank. They do convert ammonia and nitrite to less toxic nitrate but any debris, food, and waste that ends up in the filter is still in the system and needs to be removed. It's the same as if it were laying on the bottom of the tank so up the filter maintenance too.
100% agree with
Jjaws7777 above. It's even more important in smaller tanks like you have - there's less wiggle room with water quality.
Most poly members here feed every other day. Fish can go a week (or more) without food without issue. Overfeeding causes more problems than underfeeding in the hobby.
I bet you'll get back on track quickly with your feeding schedule change. I know it's frustrating to have multiple problems pop up... new tanks always seem to have those phases. Good luck!