Function run 

pub async fn run(
    state: &AppState,
    block_id: String,
    source_tab_id: String,
    source_workspace_id: String,
    target_tab_id: String,
    target_workspace_id: String,
    dst_index: Option<u32>,
) -> Result<Value, String>

Run the RedockFloatingPane saga. On success, returns { "block_id": "...", "target_tab_id": "..." }.

dst_index defaults to the end of the target tab’s blockids if callers don’t have a specific drop position (Phase 4a MVP). Phase 4b polish will let callers specify a drop position relative to a target leaf + direction (left/right/top/bottom/into).