Where do you live?
I’d wager that not many places in the USA have that kind of arrangement!
I live in a city just south of Kansas City, MO that was platted in 1860-something. I am a recovering planner, and I am amazed, and puzzled, that you both have public access (sidewalks) across your private property. Now, in Kansas City, the city fixes the sidewalk and bills the property owner, but I think that’s a function of their charter, it’s not state law.
Here in the Midwest, the right-of-way for a normal residential street is either 50 or 60 feet. The actual paved surface (back-of-curb to back-of-curb) is either 28 or 36 feet, hopefully, if the surveyors get it right, centered in the 50/60 feet,with the remaining right-of-way on either side being used for sidewalks and utilities. The adjacent property owners is responsible for cutting the grass between the sidewalk and the curb, but they do not own it, or pay taxes on it.
There are exceptions, of course, but those occur more in your “new town”, high density developments, not typical subdivisions.
Does your property line extend to the curb of the street? Are there utilities (water, sanitary sewer, storm sewer) next to curb and, therefore, also on your property?