A lot of the documents are formalities to allow them to treat you, file insurance, etc.

Your situation is not a problem. For a very few jobs a mental health event is an issue, but for the vast majority it is not. Seeking care is not unusual and is a sign of strength and not weakness.

You state you are a green card holder at this time. You have nothing to worry about; they are not going to deport you. Your citizenship is not in question.

Be sure you follow up as recommended and take your prescribed medications. Do not fall into the alcohol or other drug trap. Attend support group if recommended.

Register with your state's unemployment agency. Job loss happens more now than in the past. Keep a positive attitude. Expect your next job to be better than the one you lost.