Can they use 23 money for the 24 car?
Now that's an interesting question Andy, in the strict sense a big NO!
Teams have to account for wind tunnel, CFD & fabrication according to year stuff is for, especially if it's the following year. They won't want to go over budget in 23 so will allocate stuff automatically to 24 if it's not going on car this year.
There must be some slippage or mis reporting, but probably only minor, FIA can ask for documents, computer logs & other stuff to verify which is for what - so to speak.
We'll still see upgrades for most teams at coming races, as Toto says things are in the pipeline. It often takes time to bring new upgrades to cars, Sim work and computer time to validate worth & then fabrication time followed by more testing in practice sessions & Sim before signing off an upgrade for race use.
However if 24's car is a further iteration of the chassis/aero/wings, etc from 23 then they will keep bringing upgrades/parts this year as long as cost cap allows since the extras will be relevant to the 24 car - but crucially come under 23 budget.
In reality I guess most teams will be looking for a new path in 24 since Red Bull are so dominant. Leading teams wont catch Red Bull up with a 23 B spec car, or even a 23 C or D.
Ironically perhaps Red Bull are the only big team who can get by with a 23 B or C spec for 24. Will they though? Who knows? They pulled a suprise this year with a totally new chassis concept, so why not next term.