What the banging actually is
That bang is delayed ignition. Gas flows into the burners, but the flame doesn't catch right away. For a second or two, gas keeps building. Then it all lights at once with a small explosion.
You're hearing a controlled fireball happen a beat too late. It's the same physics as a gas grill you left on too long before hitting the igniter.
The power outage is the trigger, not the root cause. When your furnace comes back to life, it runs a full cold ignition cycle. That cold start is harder on the burners and igniter than the short cycles they run all day.
So a furnace that was quietly limping along with dirty burners suddenly gets exposed. The outage forced a hard restart, and now the problem is loud enough to scare you (as it should).
Why it's happening
Four things cause delayed ignition, and after an outage, two of them jump to the top of the list.
Dirty burners are the most common. Over a couple of seasons, rust flakes, dust, and even spider webs partly block the burner ports. The flame can't spread evenly across all the burners, so it dawdles while gas piles up.
A weak igniter is the next suspect. Hot surface igniters wear out. One that's a little late every cycle gives gas time to collect. A cold restart after an outage pushes a marginal igniter over the edge.
Then there's the outage itself messing with electronics. A surge or a series of flickers can scramble the control board or knock the gas valve timing slightly off. A full reset sometimes clears this.
Lower on the list: gas pressure dips when a whole neighborhood restarts at once, and a cracked heat exchanger from months of undiagnosed delayed ignition. That last one is the scary one, and it's why we don't shrug this off.