I personally don’t care for our definition of habitable.
I think of Mars as habitable in the sense that we’re technologically advanced enough to survive and even thrive there if only in domed habitats. In a few hundred years we may be technologically advanced enough to restart the nuclear furnace at the core of Mars and start rebuilding an atmosphere.
Humans are the most adaptable species ever to exist on the face of the planet. We can adapt to things slightly outside our required parameters. The technology of today and the future can greatly expand those parameters.
And as in your scenario, constructing an artificial atmosphere in order to allow habitation, would itself prove that the native setting is not suitable for our existence.
By your definition it is the artificially devised environment supporting life, and perhaps technologically achievable, still, it is not the native one and doesn't imply Mars is then inhabitable.