I know there's a rule saying that heroes class cards are readied when the hero activates (and not during Status phase), but what about Mission Setup ? Are those cards exhausted or readied when round 1 begins ? I couldn't find the answer in the Mission Setup section of the RRG

They start ready.

Everything enters the game ready unless said otherwise.

So heroes can get one 'free' use of their exhaustible class cards if they get to use them before their first activation.