I am working on a book that features a form of "colonization" by destroying all life on a planet by basically doing on a large scale of what a "fuel-air-bomb" does. My question is what would be the outcome of this, and would the atmosphere be intact and "usable" to human colonists?
There would be still be an atmosphere.
The majority of the gases are not going to be moving faster than escape velocity so they are going to still be there.
The atmospheric makeup will change considerably, I would assume almost no free oxygen would remain un-combusted with a similar increase in CO2 levels, and with no biosphere remaining it would stay that way. You would also have huge amounts of dust as well as water vapor added to the atmosphere.
It would be a very turbulent atmosphere for a long time, all the energy from the explosion has to go somewhere. Think runaway greenhouse gases meets nuclear winter, with planet wide hurricanes and no breathable oxygen. Not a nice place to visit or colonize.
Also as mentioned in the comments, given an ocean of any depth life would likely survive in the ocean, although not necessarily for long give the planet wide super storm.
I would personally choose a very large gamma radiation blast for sterilizing a planet. (possibly aimed exhaust from a tuned fusion rocket?)
The impact event that killed the dinosaurs broiled the land. Try using that as your model: produce heat from kinetic energy, not by burning something. That doesn't act chemically so doesn't change the composition of the atmosphere.
As I recall, the debris from the primary impact re-entered the atmosphere all over, blanketing the world, and getting very hot.
So, drop a load of gravel, or a rock that breaks up into such as it crosses the roche limit on a hooked trajectory, and have a lot of infalling objects optimized to heat the air rather than causing a crater or a single blast. Figure converting all the initial gravitational potential energy into heat.
Now it's said that dust from an impact, lingering in the atmosphere for years, would block the sun and cause an impact winter. So make that part of the extinction plan, or carefully choose your composition to settle out quickly.
The infall could also be something that's toxic to earthlife but no problem to the colonists. Imagine the dust settling out was loaded with arsenic for example.