Not yet a medical professional here, but I'm in my final year of medical school (~12 months until I get the MD) and just coming off two months on inpatient psychiatry. You're pretty much spot on. DSM-V (the latest version of the definitive psychiatry manual) defines a diagnostic criteria for major depressive disorder (At least five of the following for a period of two weeks or greater - Depressed Mood, Decreased Interest, Weight Loss/Gain, Sleep issues, Psychomotor Agitation, Fatigue, Worthlessness, Concentration Issues, and Suicidality), but oftentimes in the clinic, mild/moderate/severe depends on symptoms and the severity of functionality in the patient. Different hospitals and clinics do it differently, but what we did in the hospital to decide between mild/mod/severe was some version of the following:
First Group of Symptoms: Depressed Mood - Loss of Interest in Activites - Reduced Energy
Second Group of Symptoms: Guilt - Sleep Issues - Appetite Issues - Suicidality/Homicidality - Pessimistic Thoughts - Decreased Self-Esteem
Mild = 1+ from the first group w/ 1-2 from the second group and overall functional impairment seems "mild"
Moderate = 1+ from the first group w/ 2-3 from the second group and overall functional impairment seems "moderate"
Severe = All of the first group w/ 3+ in the second group and either severe impairment, psychosis, recent suicidality, or intent to harm self/others.
It wasn't a hard and fast rule, but rather general guidelines. In addition, we'd also evaluate functional status via asking about their lifestyle - social stressors, relationships, work, academic performance, etc.
Kaladin could definitely fit into severe, but one could also make a case for moderate when he's not frankly suicidal (which honestly may be less about depression and more about the terrible situation he was in).