Since AnkiMobile doesn’t support Shortcuts (which would be amazing, but probably a big undertaking ;)), a sensible way to interact with it is to use
anki:// scheme. The only thing I’m missing is something like
anki://x-callback-url/review?deck=<Name>. If possible, a combination of
anki://x-callback-url/review?deck=<Name>&syncPrior=true would be even better.
I’m currently running a shortcut that opens
anki://x-callback-url/sync (and few others like DND mode) upon controller connection. That way I can quickly jump into review of a deck.