Even if you covered the target in dielectric mirrors specifically engineered for the wavelength of the laser, assuming such a thing was even feasible on a cost, weight, and functional basis for the target, you would have to keep them spotlessly clean in an operational military environment for them to be effective — an impossible task.
Hence why the military doesn’t concern itself with shiny targets. At the power levels they target, nothing real can be sufficiently shiny as a matter of practical physics.
An ablative heat shield can be more effective, although that adds weight and interferes with sensors. Spinning the target can also help a little by spreading the heat across a wider surface area.
In fact, using a high-power laser to punch a hole in the atmosphere, essentially creating a functional vacuum by superheating the atmosphere in the beam path, is an old school engineering trick for exotic systems. Though in those cases, they tune the laser so that it gets absorbed by the atmosphere (similar to the gas you are suggesting). The use case is roughly analogous to employing supercavitation on torpedos.
Less because of any sort of reflective countermeasure and more because it takes way less power and precision to attack the delicate integrated electronics within a drone then it does it attack it's physical integrity.