Either you're a teacher, or you're are psychologist. Pick one.
Do not expect teachers to magically know how to be psychologists, and be able to perform that profession--along with their own--for 20 students at a time. A fully trained child psychologist has dedicated themselves to studying their profession through 7 years graduate school and has been licensed by their state and has professional certification.
"Non-cognitive" skills; such as grit, resilience, self-control, and emotional intelligence; are skills most kids will pick up naturally. If a child is having trouble with these, then they should be referred to a psychologist.
Teachers should be trained to know when a child might need to be seen by a psychologist and make that recommendation, but they should not be asked to do what they are clearly not trained to do. Nor should they be graded based on their student's progress in gaining skills they are not trained to teach.