Mars' (almost non-existant) atmosphere is mostly CO2, and you could use that, except that a CO2 level above 10% is lethal for humans and at 10%, it's still too oxygen rich.
Nitrogen has the advantage that it's inert and non-lethal.
However people can wear breathing masks when outside of buildings. Plants cannot. Most terraforming proposals focus on supporting surface plant life, and plants thrive in high-CO2 environments. These proposals involve toxically high (for humans) level of CO2 in order to support lush plant life. Once the O2 and temp gets high enough, people can survive on the surface without space suits, so long as they carry a bottle of oxygen and a breathing mask.
Longer-term, atmospheric pressure could be supplanted with a couple of Kuiper Belt objects consisting of frozen nitrogen and organics. Let it burn up in the thickening atmosphere and contribute to the developing pool of gases.
Which requires supply from somewhere. How far you can go with ISRU depends on how big the colonisation development gets.
But even without access to such deposits, fixed nitrogen in the form of ammonia could be brought from earth in sufficient quantities to support each settler. Organic waste would be composted and thus the nitrogen recycled with very little loss. N2 waste produced by decomposition would be recaptured by the atmospheric regulators, and either fixed by certain plants brought for that purpose, or industrially fixed by an arc or Haver-Bosch process in the bigger cities.
If you didn't have nitrogen you would need another inert gas to make up 80% (or whatever) of the atmosphere you were going to make.
Being in a pure oxygen environment does not have a long term impact on animals… if the pure O2 environment is 0.21 atm oxygen. There’s a long history of biological experimentation done by space agencies on this, and the Apollo missions operated on a 0.2 atm pressure for the duration of their missions. Apollo 1 famously had trouble not because it was pure O2, but because it was 1.2atm O2.
There is no reason you need backfill inert gasses to have 1.0 atmospheres.
The vast majority of the biomass on earth, including about half of the fixed nitrogen in your body was synthesized industrially via the Haber-Bosch process over the last 100 years.
Aside from those nitrogen fixing bacteria whose output we have already surpassed with industrial processes (artificial fertilizer), inert nitrogen plays no role in biological metabolism. It is not needed, at all.
Mars colonists can import nitrogen, or mine fixed nitrogen from the few deposits that are known to exist. It doesn’t need a massive atmospheric reservoir.