Bays and people are two different questions
The board can be read as columns of spaces or as columns of colleagues, and switching between the two changes nothing about the plan. A job carries both, because a bay without someone in it finishes no car.
A day holds a number of hours, and the board counts them
Available hours per day are derived from who is working, with time off subtracted rather than remembered. When a day fills up you get told, and it stays a message: you can still overload a day deliberately, because sometimes that is the right call and software should not pretend otherwise.
Work without a date stays where you can see it
Anything approved but not yet placed waits in one visible tray instead of in somebody's head. Dragging it onto a day is the whole booking step, and a job that nobody ever drags is a job you can see is not moving.