It's hard to say without knowing the details of the contract. I highly doubt Constellation put themselves in a position to be vulnerable to cost overruns. Or perhaps they see the deal as a shiny pendant they can dangle in front of dumb PE money when they want to cash out in the future.
Trust me, cynicism is well warranted with these ancient plants.
All of the articles say the deal is Microsoft agreeing to buy power for 20 years. It's possible that's wrong/incomplete, but it would be weird. Constellation's stock rose 20%, so the market at least thinks they'll make decent money on it.
And it may be an "ancient plant" but it was operational 5 years ago, under Constellation's management.
Are you suggesting Constellation will be surprised at the hidden costs?