I think this would require much less oxygen than creating a breathable atmosphere and at the same time would not limit the colonists to the inside of their dwellings.
Besides liquid breathing, fluorocarbons have other wonderful properties:
- They are very potent dielectrics unlike water, so no short-circuit.
- They have high weight so they can form an atmosphere where there is not enough gravity to keep an atmosphere of lighter gases.
- For terraforming a planet: PFCs are not photodissociated, having highest lifetime in the atmosphere, they are the most potent greenhouse gases (tetraflourocarbon is 6500 times more potent than CO2), which allows to warm up planets such as Mars (this has been already suggested).
- PFCs can be used as blood substitutes and have anestetic properties. Oxygen-rich PFCs help to heal wounds. They are also used to store living organs for transplantation.
- Some PFCs are extremely hydrophobic
As uhoh suggests in a comment, one scenario for breathable liquid environment is "walking on the ceiling":
if the local gravity were $g′$ and the perfluorocarbon had a density of 1.6 $ g/cm^3 $ then they'd be walking on the ceiling feeling a "gravity" of 0.6 $g′$.
edit: Here is an example of such a buoyant, inverted "ice walker" - starts at 03:27: