Is the air we breathe part of the public trust?

I think there is a danger in speaking like this. Being a public trust is a legal function and socially constructed idea not a material or objectively valuable thing. That isn't to say it isn't valuable, but if we speak about lawyers as if they are discovering some hidden truth about the how the law is supposed to be within the law itself, I fear we are revering our political machinations as a prime directive.

is the state government failing in its obligation to ensure our air remains viable for future generations?

The government has no obligations. It is not a single entity. If we revere it as one entity to place all responsibilities upon, we become dis-empowered. The government is fundamentally an arrangement of different individuals with different values and agendas managing a flow of resources. It should be used as a tool.

I don't say this to undermine the necessity of legal action, only to say that if you want to make the system more functional for fulfilling your values, you should recognize who is your ally and who is your enemy. There are people in the government structure involved in positive environmental change, and those totally against. I think it is best to place responsibility on those who are responsible and not let them be obscured from view under a blanket of amalgamated compromise of the good.

Another aspect I wouldn't want to leave out is one of personal responsibility. I often see a finger pointed at higher authorities and agencies as an excuse to act with negligence and disregard the systemic results of one's own actions. Your actions in your daily life matter. By consuming products or participating in systems and businesses that destroy the environment means you are condoning it. Consume ethically and responsibly.