Elysian----what kind of "hope" are you looking for, specifically.
I would say that if he is really serious about recovery, that he will throw everything that he has at it. At this point, I would expect that he would be attending AA every day---by phone or Zoom, or whatever, if Covid prohibits in person. He should have communication with his sponsor very, very, frequently. His depression needs to be evaluated by a psychiatrist---as there are different etiologies of depression and each person is different. It is too complicated for any of us to make comments on HIS depression.
I am a medical provider, myself, and I have known many recovering alcoholics who take medications for depression.
Having said that---it is not uncommon for alcoholics to be moody and have mood swings and problems of regulating emotions---especially the first year of sobriety. His symptoms seem to be more than just that.
Since you have decided to get back into the relationship with him---this puts you smack in the middle of his alcoholism---his moods---his struggles. How can you not be, when in an early romantic relationship?! His struggles become your struggles. If you push him---conflict begins to occur. This is the problem of relationships--especialy newer ones, during the early recovery period.
Idealy----you should not be discussing very much about his alcoholism and his mental state---he has a LOT of other resources that he should be taking it to,
AA members--his sponsor----his medical doctor---and his psychiatrist (for evaluation of depression/medications or not).
If you decide to stay in the relationship---I suggest that you get as much support and help for yourself as he does---as you will need to know how to detach yourself from entanglement in his problems.