The building was completely torn down and replaced by The Girls' School of Austin in 2013.

Well I'm no authority, but I've always heard them called frontage roads in the Austin area, and most of the existing map services refer to the frontage roads as, well "frontage roads." But I checked the City of Austin's Street Centerline database, and that system has no mention of "frontage roads," only the "SVRD" street designation. TxDOT seems to call them frontage roads in their materials, and they have more influence than COA. So I'd personally stick to using "frontage road," partly to differentiate between the OSM Service Road and a freeway frontage road, but also because the state calls them that.

Adding link to Street Centerline Map: https://data.austintexas.gov/Locations-and-Maps/Street-Centerline/m5w3-uea6