I was finding the main AC screen popping up in background when using shortcut * on wheel a bit annoying - and random, so tried a few button combinations to work out exact functionality - the logic I think MG were using, and I now believe it actual works ok... (not great, but ok)
The full AC screen opens in background ONLY when AC system is initially switched on, to allow changing of any/all preferences, after page is closed, selecting * will only open and toggle on/off the submenu to adjust temp/fan speed, it doesn't bring up full AC page again unless system transitioned off/on again.
Also when first starting car the full AC screen pops up - but ONLY if the AC system was powered on when I last switched off car, presumably for same reason - to select personal settings.
My two actions now to reduce the faf is leaving fan/heat on at low background level and switching AC off before turning car off.
(note I'm using term AC to refer to full HVAC system realising it's only one part of it)
This is how the system works for me with MY23 Trophy running R46 software anyway, it may differ on other variants.