Mounting the rescue effort was basically an all-hands-on-deck situation, and Picard was promoted specifically to lead that effort. If he's already an admiral in Lower Decks season three, that means the effort has already begun, and it wasn't like the situation was under wraps--kinda difficult when you're mobilizing most of the fleet for a single task and trying to figure out a way to ramp up production of tons of specialized ships on top of that. I'm assuming the Cali-class isn't involved directly because someone has to keep the Federation running.
It does beg the question of why Command wanted to get rid of a whole class of ship, though. They really couldn't afford to and things will only get worse from here until the Mars incident.
I'm thinking Season Four will probably mention it.
That is yet to be confirmed on screen though - was just in the press pack - so they could adjust the specifics of it.