I've been doing some reading about all-road / adventure-ready bikes and I'm leaning toward the Trek SL5. I weigh 265lbs and the official specs say the total weight limit for bike, rider, and cargo is 275lbs. What would realistically happen if I end up getting the bike and ride on it for long distances over time?
You may start breaking spokes in the rear wheel after putting some miles on the bike. That seems to be where the effects of load shows up first.
You can plan to mitigate this by budgeting for a new rear wheel. If this is the bike you are talking about it has 28 spoke wheels. You'll want a 32 or even a 36 spoke replacement wheel, hand built.
You don't have to get the beefier wheel straight away, but when you break a spoke don't bother getting it replaced, more will inevitably follow. Upgrade the whole wheel at that point.