I Unsure, welcome
It's a common topic - 'How do you help someone that doesn’t want to be helped?" and the answer to it never changes. It is not your responsibility to pressurize him to get help nor is it up to you to carry his burden of unhappiness. The Defense forces have all the medical help they need (I'm ex RAAF) so that isn't an issue, it's even free for them.
I suggest, from what you have written, that he is indecisive on the topic of you both as a couple. The Navy environment is such that he might be observing his sailor mates single and carefree while he is committed. The grass is greener on the other side for many.
It isn't easy living on hope when he states words that confirm much doubt. IMO breaking up with him, if it makes it worse then it wasn't meant to be, if it makes it better then there is a chance. It will be a testing time but one that is necessary to remove you from lingering in the middle.
I hope you find happiness but it's your actions that will help you find it, not only hoping.