Great thread idea. I was inspired to reply after a long time lurking.
From personal experience, no, I did not have confidence in the military system. We lost an aircraft and crew and it seemed like the base was unprepared for that contingency, especially when it came to the mental health of other aircrew.
For the TL;DR version: the bro network and an outside mental health provider (who was prior Army infantry) helped me quite a bit. So did flying; it was one of the things that was a reminder of the good times I had with those guys and kept me mentally grounded. A bunch of peers also found help through outside organizations and even the VA Mental Health personnel.
Being prior emergency services, I am a huge believer in early intervention following a traumatic event, along the CISM model, which combines mental health professionals and trained peers. It still surprises me that after two decades of war, there isn't a DOD wide effort to replicate that safety net which I positively experienced on several occasions in my civilian career.