Suppose you define possible statuses as ‘_empty’, ‘PREPARATIONS’, ‘STARTED’, ‘COMPLETED’, ‘_rejected’
You can write smth like
OR(‘STARTED’, ‘COMPLETED’, ‘_rejected’),
and the condition remains TRUE after you reach ‘STARTED’ stage
but you have other issue (even with your formula) - when you open the table tomorrow, and next days, started_date will update every date, and it’s meaning became nonsense.
formula is dynamic. if you want to create some static value, you may add checkbox field “start” (and hide it, if needed), and set “Start date” as ‘modified time’ of that checkbox field.
or you can use automation “When record matches condition” to put date into field.