The E-commerce advertising platforms typically sell commercial traffic through either second-price auction (SPA) or first-price auction (FPA). SPA was historically prevalent due to its dominant strategy incentive-compatible (DSIC) for bidders with quasi-linear utilities, especially when budgets are not a binding constraint, while FPA has gained more prominence for offering higher revenue potential to publishers and avoiding the possibility for discriminatory treatment in personalized reserve prices. Meanwhile, on the demand side, advertisers are increasingly adopting platform-wide marketing solutions akin to QuanZhanTui, shifting from spending budgets solely on commercial traffic to bidding on the entire traffic for the purpose of maximizing overall sales. For automated bidding systems, such a trend poses a critical challenge: determining optimal strategies across heterogeneous auction channels to fulfill diverse advertiser objectives, such as maximizing return (MaxReturn) or meeting target return on ad spend (TargetROAS). To overcome this challenge, this work makes two key contributions. First, we derive an efficient solution for optimal bidding under FPA channels, which takes into account the presence of organic traffic - traffic can be won for free. Second, we introduce a marginal cost alignment (MCA) strategy that provably secures bidding efficiency across heterogeneous auction mechanisms. To validate performance of our developed framework, we conduct comprehensive offline experiments on public datasets and large-scale online A/B testing, which demonstrate consistent improvements over existing methods.