Two governments share the name, and your contact page only claims one
The City of St. Louis and St. Louis County are separate governments, and buyers here sort them the way search does.
Locals do not use the two names loosely. Someone in University City says county. Someone in Soulard says city. A firm whose site says only St. Louis, with nothing further, reads as a firm that could be anywhere, and a reader deciding who to trust with a family matter notices that fast.
Your Business Profile address anchors where you appear in map results, and proximity carries a lot of weight. An office in Clayton and an office downtown are not interchangeable in the results someone in Florissant sees. Choose the address you actually work from, then write coverage pages around it rather than hoping the map fills the gap.
Keep off the procedural claims. City and county are governed differently, and a law firm publishing confident statements about another jurisdiction's practice is taking on risk for nothing. Say where your office sits and which areas you serve, and send procedural questions to the relevant office or to counsel.
One page doing this well beats a paragraph doing it badly on twelve pages. Name the places in prose, in the words people use out loud.