Solar prosumers, residential electricity consumers equipped with photovoltaic (PV) systems and battery storage, are transforming electricity markets. Their interactions with the transmission grid under varying tariff designs are not yet fully understood. We explore the influence of different pricing regimes on prosumer investment and dispatch decisions and their subsequent impact on the transmission grid. Using an integrated modeling approach that combines two open-source dispatch, investment and grid models, we simulate prosumage behavior in Germany's electricity market under real-time pricing or time-invariant pricing, as well as under zonal or nodal pricing. Our findings show that zonal pricing favors prosumer investments, while time-invariant pricing rather hinders it. In comparison, regional solar availability emerges as a larger driver for rooftop PV investments. The impact of prosumer strategies on grid congestion remains limited within the scope of our model-setup, in which home batteries cannot be used for energy arbitrage.