Climate and energy policy targets of the European Commission aim to make Europe the first climate-neutral continent by 2050. For low-carbon and net-neutral energy systems primarily based on variable renewable power generation, issues related to the market integration, cannibalisation of revenues, and cost recovery of wind and solar photovoltaics have become major concerns. The traditional discussion of the merit-order effect expects wholesale power prices in a system with 100% renewable energy sources to alternate between very high and very low values. Unlike previous work, we present a structured and technology-specific analysis of the cross-sectoral demand bidding effect for the price formation in low-carbon power markets. Starting from a stylised market arrangement and by successively augmenting it with all relevant technologies, we construct and quantify the cross-sectoral demand bidding effects in future European power markets with the cross-sectoral market modelling framework SCOPE SD. As the main contribution, we explain and substantiate the market clearing effects of new market participants in detail. With this, we focus on hybrid heat supply systems consisting of combined heat and power plants, fuel boilers, thermal storage, and electrical backup units and derive the opportunity costs of these systems. Furthermore, we show the effects of cross-border integration for a large-scale European net-neutral energy scenario. Finally, the detailed information on market clearing effects allows us to evaluate the resulting revenues of all major generation and consumption technology categories on future electricity markets.