As above, so below
On a part-terraformed Mars the partial pressure of oxygen could be as high as Earth's, or higher; but there would probably still be considerable amounts of CO2 about, reaching beyond toxic levels. The low N2 level might not be such a problem, except for agriculture. The challenge for future pantropists would not be to produce an anerobic human, but a strain of humanity tolerant of raised CO2 levels that would kill you or me.
Yes we will soon genetically alter humans = possibly some secret experiments are in progress. Only minor changes will be without bad side effects.
If we change Mars to 50% oxygen at 0.2 bar, possibly a few humans can remain conscious for 20 minutes breathing that air. A few whiffs of 99% oxygen may keep them conscious a few more minites. That likely is about the limit without genetic changes with big disadvantages. A few humans have survived inside the Arctic Circle for 1000 plus years. If we warm Mars so it is usually Arctic winter temperature, then some people can work outside for 20 minutes, longer with electric socks and electric underware. The radiation will produce shorter life expectancy and more health problems, but they likely can produce children before they die, if they limit outdoor exposure to about one hour per day. The 0.38 gravity will likely mean they cannot return to Earth except as a cripple, but will be ok on Mars with a good exersize routeen. Toxic material in the soil will likely require lots more caution than Earth dirt. I'm guessing. Neil
Terraforming takes eons to complete, so there'd be plenty of time to figure out bioengineering.