You can only get the drinks they list specifically for HH, which are the cheapest grade of alcohol. None of them will be over $10 drinks. In other words, this perk is useless if you have a drink package.
With the possible exception of Eden, I view Celebrity's specialty restaurants as a step down from the MDR. In general, they would have to pay me to eat in one.
Even though they restrict certain things like shorts and tank tops, I've seen people wearing pretty much anything. Celebrity does not enforce any dress standards.
I prefer raw, but that's not a complimentary option (and the sushi quality on Celebrity is not really up there). My best breakfasts ever have been at Tsukiji Fish Market in Tokyo.
We've never sailed on a ship with a Retreat Deck, and don't use Michael's Lounge because it's just a crowded, dark, dingy room. For us, it's Luminae and space.
Since we've been booking suites lately, the only real Zenith perk that matters (to us) is the free laundry (not interested in either Bermuda or Caribbean cruises), and we can usually get by pretty well with the four bags at Elite Plus. So very little reason to strive for Zenith anyway.
And my experience is that the app will not be accurate ever. We've been on cruises where the app showed no entertainment, or showed activities going on that never happened, or showed imaginary menus. If you trust the app for anything, you are being foolish.
I thought we might eventually make Zenith, but with Celebrity's rapidly declining value proposition, I expect to be booking other lines even more and will probably just languish at Elite Plus.