Function click_element 

pub async fn click_element(
    __arg0: State<Arc<AppState>>,
    headers: HeaderMap,
    __arg2: Json<ClickElementReq>,
) -> (StatusCode, Json<ApiResponse<AckData>>)

POST /agentmux/browser/click_element — synthesize a real mouse click on the first element matching selector. Dispatches Input.dispatchMouseEvent (mousePressed + mouseReleased) at the element’s centroid.

Note: this is a “real” mouse event, NOT a DOM .click() — so :focus-visible, pointer-related listeners, and the pane’s Win32 focus-routing behave identically to a human click. That’s why the stress test uses this rather than eval’ing .click().