The idea of total distance in a city has been discussed loosely a couple times (here & here) but is not currently available.
I’d recommend checking with your local government body (city, country, council or equivalent) to see if they have a ‘Planning’ department. Sometimes these departments will have not only a map of current (and future proposed streets) but they may also have done a survey where they measured every street in the city. Even with a known total distance, it doesn’t mean that will be the total distance you will run. There will be certain inefficiencies like dead ends where you are running the street distance twice or where you need to repeat part of a street to get to another street.
For example, my city did have a document that had the total distance of all streets measured out (though it’s a couple years old). It listed 772.35 miles/1242.94 km. Each run I did, I labeled with a specific name so that way I could aggregate the total distance & elevation at the end. When I completed my city, the total running distance was 1916.7 miles/3084.62 km.