If the food is cold, refrigerator cold, you should be fine.
Am surprised that after 24 hours everything was defrosted. We have been without power for over 48 hours and the stuff was still frozen.
One thing we have done when expecting a possible power outage (a hurricane for example) is buy ice. Also we turn the thermostat in the fridge and freezer to a lower temperature.
If we lose power unexpectedly we beeline it to a store that sells ice (ya gotta be fast, most people just wait for the power to come back on. By the time they figure out it is going to be a while, the ice has been sold to the early birds.) And then we stuff as much ice as we can in the fridge and freezer compartments.
We also fill some coolers with ice into which we toss some food and drinks that we remove from the fridge/freezer as we are packing in the ice.
Once the fridge is engorged with ice we do not open the doors again, unless there is a very compelling reason.
We live from the cooler, the pantry, any groceries (if open), and cook on the gas stove, when we have one, or the grill. No way to heat a hot meal? Try take out. If it is a regional power outage, many places may be closed.
But try a pizzeria. They have gas stoves and their refrigerated ingredients are just going bad. And so they may open up, even if they have no electricity.
Pizza is, after all, a hot meal. The leftovers are cold but you can always open up a cool beer from the cooler, chomp down on a cold slice, and tell stories about when you were a fledglling and cold pizza and beer constituted two of the four basic food groups.
May not sound exciting, but there ain't no TV.
Sorry, am getting off topic.
If the food is thawed cool, and you don't feel comfortable about refreezing, ya gotta cook it. And great ideas have been given. Once cooked you can then refreeze with impunity.
Just some Friday night rantings. But that is our approach to a power outage.
Take care and God bless.