is there a MyChart app for MacBook Air?

No. See the following from https://www.providence.org/services/providence-app

• The Providence app is your personalized connection to the great care and services we’re known for. It is available for iPhone and Android devices.

It is very very common that apps are offered for mobile devices only and that to access similar functionality on a computer you use an internet browser. The following may be their website for that: https://mychartor.providence.org/mychart/Authentication/Login?

No, there is no app, but it is just as easy to sign up/establish an account using your browser and bookmark the sign in page. I've got bookmarks for Providence and four other MyCharts.