I’ve never heard of property tax rates based on your floor covering.
Hard wood floors cost more than wall-to-wall carpet, thus your tax assessment is increased.
It all depends upon the building codes and property taxes for your local jurisdiction. Some do, and some don't. The greedier governments interfere with builder-owner choices by arbitrarily slapping taxes on necessities and/or luxuries.
After Britain lost the American colonies in the Revolution in part over taxation policies, they levied a series of ruinous taxes at home in Britain. The government began taxing the number of windows with glazing, so the taxpayers began to replace window glass with paper, cloth, and other alternatives. The government responded by taxing windows, so the taxpayers bricked up and boarded over the windows. The government then dictated building codes that required a certain number of windows, which then could be taxed.
In some places, it's a fight over whether or not the square footage of a garage or other space is taxed at all or taxed at the higher rate based upon whether or not it is a structure attached to the house or detached from the house.
Farmers have been taxed out of business by county governments basing the tax rates on arbitrary assumptions about how much income the land should produce. A farm with little tillable and grazable acreage and extensive woodland with uneven topography is taxed at a rate higher than any possible profit from a crop could produce. In answer to complaints the county government suggests more efficient usage of the acreage by clearcutting the woodland to cultivate land and soil not suitable for cultivation. The same government authorities then complain about the loss of forest habitat and its effect upon the environment. Duh!